Finite Group Databasebeta

← Group #13155625

Character table — Group #13155625

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11112222222222222244444444444444444488888888888888999912121212121212121212121212121818181818181818181818181818242424242424242424242424242424242424242436363636363636363636108108
order12223334466666666633366666666612121212121236661212121212121212121244442244441212121212121212448888888812121212666666661212121212121212121212121212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ511111111111111111111111111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111
χ911-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-1111-1-1-111-1-1111-1-11-111-1-1ii−i−i1-11-1i−i11-1-1ii−i−ii−i11-1-1ii−i−iii−i−i11-1-111-1-1i−i1-1ii−i−i11-1-1i−i11-1-1ii−i−ii−i
χ1011-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-1111-1-1-111-1-1111-1-11-111-1-1ii−i−i1-1-11−ii-1-111−i−iiii−i-1-111−i−iiiii−i−i11-1-111-1-1−ii-11−i−iii-1-111i−i-1-111−i−iiii−i
χ1111-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-1111-1-1-111-1-1111-1-11-111-1-1ii−i−i-111-1i−i11-1-1ii−i−ii−i-1-111−i−iiiii−i−i-1-111-1-111i−i1-1ii−i−i11-1-1i−i-1-111−i−iii−ii
χ1211-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-1111-1-1-111-1-1111-1-11-111-1-1ii−i−i-11-11−ii-1-111−i−iiii−i11-1-1ii−i−iii−i−i-1-111-1-111−ii-11−i−iii-1-111i−i11-1-1ii−i−i−ii
χ1311-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-1111-1-1-111-1-1111-1-11-111-1-1−i−iii1-11-1−ii11-1-1−i−iii−ii11-1-1−i−iii−i−iii11-1-111-1-1−ii1-1−i−iii11-1-1−ii11-1-1−i−iii−ii
χ1411-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-1111-1-1-111-1-1111-1-11-111-1-1−i−iii1-1-11i−i-1-111ii−i−i−ii-1-111ii−i−i−i−iii11-1-111-1-1i−i-11ii−i−i-1-111−ii-1-111ii−i−i−ii
χ1511-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-1111-1-1-111-1-1111-1-11-111-1-1−i−iii-111-1−ii11-1-1−i−iii−ii-1-111ii−i−i−i−iii-1-111-1-111−ii1-1−i−iii11-1-1−ii-1-111ii−i−ii−i
χ1611-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-1111-1-1-111-1-1111-1-11-111-1-1−i−iii-11-11i−i-1-111ii−i−i−ii11-1-1−i−iii−i−iii-1-111-1-111i−i-11ii−i−i-1-111−ii11-1-1−i−iiii−i
χ172222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2222200000000000000-2-200000000222200000000000000000000-2-20000000000
χ182222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000002200000000-2-2-2-200000000000000000000220000000000
χ19222222-12222-1-1-122222-1-122-1-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1000022002200002222000000222200002-12-1-1-1-1-1-1-100-1-1-1-10000000000-1-1-1-100
χ20222222-12222-1-1-122222-1-122-1-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-100002200-2-20000-2-2-2-2000000-2-2-2-200002-12-1-1-1-1-1110011110000000000111100
χ21222222-12222-1-1-122222-1-122-1-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-10000-2-2002200002222000000-2-2-2-20000-21-211111-1-100-1-1-1-10000000000111100
χ22222222-12222-1-1-122222-1-122-1-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-10000-2-200-2-20000-2-2-2-200000022220000-21-211111110011110000000000-1-1-1-100
χ2322222-1222-1-12222-122-12-1-1-12-1-12-12-1222-12-1-1-1-1-12-12-1-1-1-1-1-1-100002222002222000000222200000000-12-12-1-1-1-100-1-10000-1-1-1-100-1-1-1-1000000
χ2422222-1222-1-12222-122-12-1-1-12-1-12-12-1222-12-1-1-1-1-12-12-1-1-1-1-1-1-1000022-2-200-2-2-2-2000000-2-2-2-200000000-12-12-1-1-1-1001100001111001111000000
χ2522222-1222-1-12222-122-12-1-1-12-1-12-12-1222-12-1-1-1-1-12-12-1-1-1-1-1-1-10000-2-222002222000000-2-2-2-2000000001-21-2111100-1-10000-1-1-1-1001111000000
χ2622222-1222-1-12222-122-12-1-1-12-1-12-12-1222-12-1-1-1-1-12-12-1-1-1-1-1-1-10000-2-2-2-200-2-2-2-20000002222000000001-21-2111100110000111100-1-1-1-1000000
χ272222-1222222222-12-1-1-1-12-1-1-122-12-1-12-1-1222-1-1-1-1-12-12-1-1-1-1-1-12222002222-1-1-1-1-1-1-1-12200000000-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-10000000000
χ282222-1222222222-12-1-1-1-12-1-1-122-12-1-12-1-1222-1-1-1-1-12-12-1-1-1-1-1-1222200-2-2-2-2111111112200000000-1-1-1-100000000-2-2-2-211111111-1-10000000000
χ292222-1222222222-12-1-1-1-12-1-1-122-12-1-12-1-1222-1-1-1-1-12-12-1-1-1-1-1-1-2-2-2-20022-2-2-1-1-1-11111-2-200000000111100000000-2-2221111-1-1-1-1110000000000
χ302222-1222222222-12-1-1-1-12-1-1-122-12-1-12-1-1222-1-1-1-1-12-12-1-1-1-1-1-1-2-2-2-200-2-2221111-1-1-1-1-2-20000000011110000000022-2-2-1-1-1-11111110000000000
χ312222-122-2-222222-12-1-1-1-12-1-1-122-12-1-1-211-2-2-2-1-1-1-11-21-21111112222000000−i3i3−i3i3−i3i3−i3i3-2-200000000-1-1-1-1000000000000−i3i3−i3i3−i3i3−i3i3110000000000
χ322222-122-2-222222-12-1-1-1-12-1-1-122-12-1-1-211-2-2-2-1-1-1-11-21-21111112222000000i3−i3i3−i3i3−i3i3−i3-2-200000000-1-1-1-1000000000000i3−i3i3−i3i3−i3i3−i3110000000000
χ332222-122-2-222222-12-1-1-1-12-1-1-122-12-1-1-211-2-2-2-1-1-1-11-21-2111111-2-2-2-2000000−i3i3−i3i3i3−i3i3−i322000000001111000000000000i3−i3i3−i3−i3i3−i3i3-1-10000000000
χ342222-122-2-222222-12-1-1-1-12-1-1-122-12-1-1-211-2-2-2-1-1-1-11-21-2111111-2-2-2-2000000i3−i3i3−i3−i3i3−i3i322000000001111000000000000−i3i3−i3i3i3−i3i3−i3-1-10000000000
χ3522-2-2222-22-2-2-22-222-2-2222-2-2-2-2-222-22-2-2222-22-2-22-2-222-22-2-2222i2i−2i−2i00000000000000−2i2i000000002i2i−2i−2i00000000000000000000−2i2i0000000000
χ3622-2-2222-22-2-2-22-222-2-2222-2-2-2-2-222-22-2-2222-22-2-22-2-222-22-2-222−2i−2i2i2i000000000000002i−2i00000000−2i−2i2i2i000000000000000000002i−2i0000000000
χ3722-2-222-12-2-2-21-1122-2-22-1-1-2-2111-1-112-12-2-212-111-1-1-1112-2-1-11100002-2002i−2i00002i2i−2i−2i0000002i2i−2i−2i00002-1-21-1-111−ii00−i−iii0000000000−i−iii00
χ3822-2-222-12-2-2-21-1122-2-22-1-1-2-2111-1-112-12-2-212-111-1-1-1112-2-1-11100002-200−2i2i0000−2i−2i2i2i000000−2i−2i2i2i00002-1-21-1-111i−i00ii−i−i0000000000ii−i−i00
χ3922-2-222-12-2-2-21-1122-2-22-1-1-2-2111-1-112-12-2-212-111-1-1-1112-2-1-1110000-22002i−2i00002i2i−2i−2i000000−2i−2i2i2i0000-212-111-1-1−ii00−i−iii0000000000ii−i−i00
χ4022-2-222-12-2-2-21-1122-2-22-1-1-2-2111-1-112-12-2-212-111-1-1-1112-2-1-1110000-2200−2i2i0000−2i−2i2i2i0000002i2i−2i−2i0000-212-111-1-1i−i00ii−i−i0000000000−i−iii00
χ4122-2-22-122-211-22-22-1-2-2-12-111-2112-1-2-122-21-2-1-111-12-1-21-11-1-11100002-22-20022-2-200000022-2-200000000-121-2-1-11100-110000-1-11100-1-111000000
χ4222-2-22-122-211-22-22-1-2-2-12-111-2112-1-2-122-21-2-1-111-12-1-21-11-1-11100002-2-2200-2-222000000-2-22200000000-121-2-1-111001-1000011-1-10011-1-1000000
χ4322-2-22-122-211-22-22-1-2-2-12-111-2112-1-2-122-21-2-1-111-12-1-21-11-1-1110000-222-20022-2-2000000-2-222000000001-2-1211-1-100-110000-1-1110011-1-1000000
χ4422-2-22-122-211-22-22-1-2-2-12-111-2112-1-2-122-21-2-1-111-12-1-21-11-1-1110000-22-2200-2-22200000022-2-2000000001-2-1211-1-1001-1000011-1-100-1-111000000
χ4522-2-2-1222-2-2-2-22-2-1211-1-12111-2-2-121-12-11-2-22-111-1-121-2-11-1-1112i2i−2i−2i002-22i−2i-1-111−i−iii2i−2i00000000−i−iii000000002i−2i2-2−i−iii-1-111−ii0000000000
χ4622-2-2-1222-2-2-2-22-2-1211-1-12111-2-2-121-12-11-2-22-111-1-121-2-11-1-1112i2i−2i−2i00-22−2i2i11-1-1ii−i−i2i−2i00000000−i−iii00000000−2i2i-22ii−i−i11-1-1−ii0000000000
χ4722-2-2-1222-2-2-2-22-2-1211-1-12111-2-2-121-12-11-2-22-111-1-121-2-11-1-111−2i−2i2i2i002-2−2i2i-1-111ii−i−i−2i2i00000000ii−i−i00000000−2i2i2-2ii−i−i-1-111i−i0000000000
χ4822-2-2-1222-2-2-2-22-2-1211-1-12111-2-2-121-12-11-2-22-111-1-121-2-11-1-111−2i−2i2i2i00-222i−2i11-1-1−i−iii−2i2i00000000ii−i−i000000002i−2i-22−i−iii11-1-1i−i0000000000
χ4922-2-2-122-22-2-2-22-2-1211-1-12111-2-2-121-1-21-122-2-111-11-2-121-111-1-12i2i−2i−2i000000−i3i3i3−i33−3−33−2i2i00000000−i−iii0000000000003−3−33−i3i3i3−i3i−i0000000000
χ5022-2-2-122-22-2-2-22-2-1211-1-12111-2-2-121-1-21-122-2-111-11-2-121-111-1-12i2i−2i−2i000000i3−i3−i3i3−333−3−2i2i00000000−i−iii000000000000−333−3i3−i3−i3i3i−i0000000000
χ5122-2-2-122-22-2-2-22-2-1211-1-12111-2-2-121-1-21-122-2-111-11-2-121-111-1-1−2i−2i2i2i000000−i3i3i3−i3−333−32i−2i00000000ii−i−i000000000000−333−3−i3i3i3−i3−ii0000000000
χ5222-2-2-122-22-2-2-22-2-1211-1-12111-2-2-121-1-21-122-2-111-11-2-121-111-1-1−2i−2i2i2i000000i3−i3−i3i33−3−332i−2i00000000ii−i−i0000000000003−3−33i3−i3−i3i3−ii0000000000
χ532-22-2222002-2-2-22-2-2-222222-2-22-2-2-22-200000022-2-200000000002i−2i2i−2i0000000000000000−i2i2−i2i22−22−22i−2i2i−2i0000000000000000000000−i2i2−i2i22−22−200
χ542-22-2222002-2-2-22-2-2-222222-2-22-2-2-22-200000022-2-200000000002i−2i2i−2i0000000000000000i2−i2i2−i2−22−222i−2i2i−2i0000000000000000000000i2−i2i2−i2−22−2200
χ552-22-2222002-2-2-22-2-2-222222-2-22-2-2-22-200000022-2-20000000000−2i2i−2i2i0000000000000000−i2i2−i2i2−22−22−2i2i−2i2i0000000000000000000000−i2i2−i2i2−22−2200
χ562-22-2222002-2-2-22-2-2-222222-2-22-2-2-22-200000022-2-20000000000−2i2i−2i2i0000000000000000i2−i2i2−i22−22−2−2i2i−2i2i0000000000000000000000i2−i2i2−i22−22−200
χ572-2-2222200-222-2-2-2-22-2222-222-22-2-2-2-20000002-22-200000000002-2-220000000000000000−i2i2i2−i2−i2i2i2−i22-2-220000000000000000000000−i2i2i2−i2−i2i2i2−i200
χ582-2-2222200-222-2-2-2-22-2222-222-22-2-2-2-20000002-22-200000000002-2-220000000000000000i2−i2−i2i2i2−i2−i2i22-2-220000000000000000000000i2−i2−i2i2i2−i2−i2i200
χ592-2-2222200-222-2-2-2-22-2222-222-22-2-2-2-20000002-22-20000000000-222-20000000000000000−i2i2i2−i2i2−i2−i2i2-222-20000000000000000000000−i2i2i2−i2i2−i2−i2i200
χ602-2-2222200-222-2-2-2-22-2222-222-22-2-2-2-20000002-22-20000000000-222-20000000000000000i2−i2−i2i2−i2i2i2−i2-222-20000000000000000000000i2−i2−i2i2−i2i2i2−i200
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χ724444-2-2444-2-2444-2-2-2-21-2-211-2-2-2-2-2-214-2-2-24-21111-2-2-2-2111111000000-4-40022220000000000000000000000000000220000-1-1-1-1000000000000
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χ744444-2-24-4-4-2-2444-2-2-2-21-2-211-2-2-2-2-2-21-4222-4211112222-1-1-1-1-1-100000000002i3−2i32i3−2i30000000000000000000000000000000000−i3i3−i3i3000000000000
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χ7644-4-44-24-4422-44-44-2-4-4-24-222-4224-2-4-2-4-44-242-222-2-424-22-222-2-20000000000000000000000000000000000000000000000000000000000000000
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χ8244-4-4-24-24-4-4-42-22-2422-21-222-1221-2-1-2-2-22-4241-1-111-2-12-2211-1-100000000−4i4i00002i2i−2i−2i00000000000000000000002i−2i00−i−iii0000000000000000
χ8344-4-4-24-2-44-4-42-22-2422-21-222-1221-2-1-222-24-2-41-1-11-121-22-2-1-1110000000000000023−23−232300000000000000000000000000−333−30000000000000000
χ8444-4-4-24-2-44-4-42-22-2422-21-222-1221-2-1-222-24-2-41-1-11-121-22-2-1-11100000000000000−232323−23000000000000000000000000003−3−330000000000000000
χ8544-4-4-2-244-422-44-4-2-2221-2-2-1-1222-2-2214-222-4-21-1-11-2-2221-111-1-10000004-400-2-2220000000000000000000000000000-22000011-1-1000000000000
χ8644-4-4-2-244-422-44-4-2-2221-2-2-1-1222-2-2214-222-4-21-1-11-2-2221-111-1-1000000-440022-2-200000000000000000000000000002-20000-1-111000000000000
χ8744-4-4-2-24-4422-44-4-2-2221-2-2-1-1222-2-221-42-2-2421-1-1122-2-2-11-1-1110000000000−2i32i32i3−2i30000000000000000000000000000000000i3−i3−i3i3000000000000
χ8844-4-4-2-24-4422-44-4-2-2221-2-2-1-1222-2-221-42-2-2421-1-1122-2-2-11-1-11100000000002i3−2i3−2i32i30000000000000000000000000000000000−i3i3i3−i3000000000000
χ894-44-444-2004-422-2-4-4-444-2-24-42-2222-2-4000000-2-222000000000000000000000000000000000022−2222−22000000000000000000000000000000−22−2200
χ904-44-444-2004-422-2-4-4-444-2-24-42-2222-2-4000000-2-2220000000000000000000000000000000000−2222−22220000000000000000000000000000002−22−200
χ914-44-44-2400-22-4-44-42-44-24-2-22-4-22-4242000000-2-222000000000000000000000000000000−2i22i2−2i22i2000000000000000000000000000000i2−i2i2−i2000000
χ924-44-44-2400-22-4-44-42-44-24-2-22-4-22-4242000000-2-2220000000000000000000000000000002i2−2i22i2−2i2000000000000000000000000000000−i2i2−i2i2000000
χ934-44-4-244004-4-4-442-42-2-2-24-2224-42-4-22000000-2-22200000000004i−4i4i−4i000000000000000000000000−2i2i−2i2i00000000000000000000000000000000
χ944-44-4-244004-4-4-442-42-2-2-24-2224-42-4-22000000-2-2220000000000−4i4i−4i4i0000000000000000000000002i−2i2i−2i00000000000000000000000000000000
χ954-4-4444-200-44-222-4-44-44-2-2-44-22-2222-4000000-22-220000000000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000000i2−i2−i2i200
χ964-4-4444-200-44-222-4-44-44-2-2-44-22-2222-4000000-22-2200000000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000000−i2i2i2−i200
χ974-4-444-24002-24-4-4-424-4-24-22-242-2-42-42000000-22-22000000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000000i2−i2−i2i2000000
χ984-4-444-24002-24-4-4-424-4-24-22-242-2-42-42000000-22-220000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000000−i2i2i2−i2000000
χ994-4-44-24400-444-4-42-4-22-2-242-2-2-442-422000000-22-2200000000004-4-44000000000000000000000000-222-200000000000000000000000000000000
χ1004-4-44-24400-444-4-42-4-22-2-242-2-2-442-422000000-22-220000000000-444-40000000000000000000000002-2-2200000000000000000000000000000000
χ1018888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-48-8444-44-4-444222-2-2-2-2-222-22-4-4444-4-111-122-2-22-2-1-1110000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-4-88444-44-4-444222-2-2-2-2-222-2244-4-4-44-111-1-2-222-2211-1-10000000000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-400-4444-4-84-88-4-42-4442-24-2-4400000022-2-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-48-4008-844-44-84-4-42-4-44-2-44-242400000022-2-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4800-44-8-88444-42-4-42-24-4444-4-200000022-2-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-400-4444-4444-42222-2-22-2-2-22-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-400-4444-4444-42222-2-22-2-2-22-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000000000000000000
χ1108-8-888-4-4004-4-444-848-8-4-424-4-4-224-2440000002-22-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-400-88-4444-8-44-42-44-424-4-24-240000002-22-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-48004-48-8-844-442-4-4-22-44-4444-20000002-22-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4004-4-44444-44222-222-22-2-2-2-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4004-4-44444-44222-222-22-2-2-2-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).