Finite Group Databasebeta

← Group #13155624

Character table — Group #13155624

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11112222222222222244444444444444444488888888888888999912121212121212121212121212121818181818181818181818181818242424242424242424242424242424242424242436363636363636363636108108
order122233344666666666333666666666121212121212366612121212121212121212444422444466661212121244888888881212121266666612121212121212121212121212121212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111
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
χ511111111111111111111111111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ911-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-111-11-11-11-1-1111-1-11-111-1-1ii−i−i1-11-1i−i11-1-1ii−i−ii−i11-1-1ii−i−iii−i−i1-111-1-1i−i11-1-1ii−i−i11-1-1i−i11-1-1ii−i−ii−i
χ1011-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-111-11-11-11-1-1111-1-11-111-1-1ii−i−i1-1-11i−i11-1-1ii−i−ii−i-1-111−i−iiiii−i−i1-111-1-1i−i-1-111ii−i−i-1-111i−i-1-111−i−iii−ii
χ1111-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-111-11-11-11-1-1111-1-11-111-1-1ii−i−i-111-1−ii-1-111−i−iiii−i-1-111−i−iiiii−i−i-11-1-111−ii11-1-1−i−iii11-1-1i−i-1-111−i−iiii−i
χ1211-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-111-11-11-11-1-1111-1-11-111-1-1ii−i−i-11-11−ii-1-111−i−iiii−i11-1-1ii−i−iii−i−i-11-1-111−ii-1-111−i−iii-1-111i−i11-1-1ii−i−i−ii
χ1311-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-111-11-11-11-1-1111-1-11-111-1-1−i−iii1-11-1−ii11-1-1−i−iii−ii11-1-1−i−iii−i−iii1-111-1-1−ii11-1-1−i−iii11-1-1−ii11-1-1−i−iii−ii
χ1411-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-111-11-11-11-1-1111-1-11-111-1-1−i−iii1-1-11−ii11-1-1−i−iii−ii-1-111ii−i−i−i−iii1-111-1-1−ii-1-111−i−iii-1-111−ii-1-111ii−i−ii−i
χ1511-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-111-11-11-11-1-1111-1-11-111-1-1−i−iii-111-1i−i-1-111ii−i−i−ii-1-111ii−i−i−i−iii-11-1-111i−i11-1-1ii−i−i11-1-1−ii-1-111ii−i−i−ii
χ1611-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-111-11-11-11-1-1111-1-11-111-1-1−i−iii-11-11i−i-1-111ii−i−i−ii11-1-1−i−iii−i−iii-11-1-111i−i-1-111ii−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
χ19222222-122222-1222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222220022-1-1-1-1-1-1-1-12200000000-1-1-1-122-1-1-1-1220000-1-1-1-10000-1-10000000000
χ20222222-122222-1222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222-2-200-2-2111111112200000000-1-1-1-1-2-21111-2-2000011110000-1-10000000000
χ21222222-122222-1222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-22200-2-2-1-1-1-11111-2-200000000111122-1-1-1-1-2-2000011110000110000000000
χ22222222-122222-1222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-200221111-1-1-1-1-2-2000000001111-2-21111220000-1-1-1-10000110000000000
χ23222222-1-2-2222-1222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-211112222000000−i3i3−i3i3−i3i3−i3i3-2-200000000-1-1-1-100−i3i3−i3i3000000−i3i3−i3i30000110000000000
χ24222222-1-2-2222-1222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-211112222000000i3−i3i3−i3i3−i3i3−i3-2-200000000-1-1-1-100i3−i3i3−i3000000i3−i3i3−i30000110000000000
χ25222222-1-2-2222-1222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-21111-2-2-2-2000000−i3i3−i3i3i3−i3i3−i32200000000111100−i3i3−i3i3000000i3−i3i3−i30000-1-10000000000
χ26222222-1-2-2222-1222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-21111-2-2-2-2000000i3−i3i3−i3−i3i3−i3i32200000000111100i3−i3i3−i3000000−i3i3−i3i30000-1-10000000000
χ2722222-12222-1-1222-122-12-1-1-12-1-12-12-1222-1-12-1-1-1-12-12-1-1-1-1-1-1-100002222002222000000222200000000-1-1-1-1-1-1002-12-10000-1-1-1-100-1-1-1-1000000
χ2822222-12222-1-1222-122-12-1-1-12-1-12-12-1222-1-12-1-1-1-12-12-1-1-1-1-1-1-1000022-2-2002222000000-2-2-2-200000000-1-1-1-1-1-100-21-2100001111001111000000
χ2922222-12222-1-1222-122-12-1-1-12-1-12-12-1222-1-12-1-1-1-12-12-1-1-1-1-1-1-10000-2-22200-2-2-2-2000000-2-2-2-200000000111111002-12-10000-1-1-1-1001111000000
χ3022222-12222-1-1222-122-12-1-1-12-1-12-12-1222-1-12-1-1-1-12-12-1-1-1-1-1-1-10000-2-2-2-200-2-2-2-200000022220000000011111100-21-210000111100-1-1-1-1000000
χ312222-12222-1222-1-1222-1-12-1-1-122-12-1-122-122-1-1-1-1-1-12-12-1-1-1-1-1-100000022220000222200000022220000000000-1-1-12-12-1-1-1-1-1-1-1-1000000-1-1-1-100
χ322222-12222-1222-1-1222-1-12-1-1-122-12-1-122-122-1-1-1-1-1-12-12-1-1-1-1-1-100000022-2-20000-2-2-2-2000000-2-2-2-2000000000011-12-121111-1-1-1-1000000111100
χ332222-12222-1222-1-1222-1-12-1-1-122-12-1-122-122-1-1-1-1-1-12-12-1-1-1-1-1-1000000-2-22200002222000000-2-2-2-20000000000-1-11-21-2-1-1-1-11111000000111100
χ342222-12222-1222-1-1222-1-12-1-1-122-12-1-122-122-1-1-1-1-1-12-12-1-1-1-1-1-1000000-2-2-2-20000-2-2-2-200000022220000000000111-21-211111111000000-1-1-1-100
χ3522-2-2222-22-2-2-22-222-2-2222-2-2-2-2-222-22-22-22-222-2-22-2-222-22-2-2222i2i−2i−2i00000000000000−2i2i000000002i2i−2i−2i00000000000000000000−2i2i0000000000
χ3622-2-2222-22-2-2-22-222-2-2222-2-2-2-2-222-22-22-22-222-2-22-2-222-22-2-222−2i−2i2i2i000000000000002i−2i00000000−2i−2i2i2i000000000000000000002i−2i0000000000
χ3722-2-222-12-2-2-2-2-1-222112-1-1-2-2111-1-112-112-22-2-111-1-1-1112-2-1-1112i2i−2i−2i2-2002i−2i-1-111−i−iii2i−2i00000000−i−iii2-2-1-1112i−2i0000−i−iii0000−ii0000000000
χ3822-2-222-12-2-2-2-2-1-222112-1-1-2-2111-1-112-112-22-2-111-1-1-1112-2-1-1112i2i−2i−2i-2200−2i2i11-1-1ii−i−i2i−2i00000000−i−iii-2211-1-1−2i2i0000ii−i−i0000−ii0000000000
χ3922-2-222-12-2-2-2-2-1-222112-1-1-2-2111-1-112-112-22-2-111-1-1-1112-2-1-111−2i−2i2i2i2-200−2i2i-1-111ii−i−i−2i2i00000000ii−i−i2-2-1-111−2i2i0000ii−i−i0000i−i0000000000
χ4022-2-222-12-2-2-2-2-1-222112-1-1-2-2111-1-112-112-22-2-111-1-1-1112-2-1-111−2i−2i2i2i-22002i−2i11-1-1−i−iii−2i2i00000000ii−i−i-2211-1-12i−2i0000−i−iii0000i−i0000000000
χ4122-2-222-1-22-2-2-2-1-222112-1-1-2-2111-1-1121-1-22-22-111-111-1-1-2211-1-12i2i−2i−2i000000−i3i3i3−i33−3−33−2i2i00000000−i−iii00−i3i3i3−i30000003−3−330000i−i0000000000
χ4222-2-222-1-22-2-2-2-1-222112-1-1-2-2111-1-1121-1-22-22-111-111-1-1-2211-1-12i2i−2i−2i000000i3−i3−i3i3−333−3−2i2i00000000−i−iii00i3−i3−i3i3000000−333−30000i−i0000000000
χ4322-2-222-1-22-2-2-2-1-222112-1-1-2-2111-1-1121-1-22-22-111-111-1-1-2211-1-1−2i−2i2i2i000000−i3i3i3−i3−333−32i−2i00000000ii−i−i00−i3i3i3−i3000000−333−30000−ii0000000000
χ4422-2-222-1-22-2-2-2-1-222112-1-1-2-2111-1-1121-1-22-22-111-111-1-1-2211-1-1−2i−2i2i2i000000i3−i3−i3i33−3−332i−2i00000000ii−i−i00i3−i3−i3i30000003−3−330000−ii0000000000
χ4522-2-22-122-2-2112-22-1-2-2-12-111-2112-1-2-12-221-1-2-111-12-1-21-11-1-11100002-22-20022-2-200000022-2-200000000-11-1-111002-1-210000-1-11100-1-111000000
χ4622-2-22-122-2-2112-22-1-2-2-12-111-2112-1-2-12-221-1-2-111-12-1-21-11-1-11100002-2-220022-2-2000000-2-22200000000-11-1-11100-212-1000011-1-10011-1-1000000
χ4722-2-22-122-2-2112-22-1-2-2-12-111-2112-1-2-12-221-1-2-111-12-1-21-11-1-1110000-222-200-2-222000000-2-222000000001-111-1-1002-1-210000-1-1110011-1-1000000
χ4822-2-22-122-2-2112-22-1-2-2-12-111-2112-1-2-12-221-1-2-111-12-1-21-11-1-1110000-22-2200-2-22200000022-2-2000000001-111-1-100-212-1000011-1-100-1-111000000
χ4922-2-2-1222-21-2-221-12-2-2-1-12111-2-2-121-12-2-1-221-111-1-121-2-11-1-1110000002-22i−2i00002i2i−2i−2i0000002i2i−2i−2i0000000000−ii-121-2−i−iii-1-111000000−i−iii00
χ5022-2-2-1222-21-2-221-12-2-2-1-12111-2-2-121-12-2-1-221-111-1-121-2-11-1-1110000002-2−2i2i0000−2i−2i2i2i000000−2i−2i2i2i0000000000i−i-121-2ii−i−i-1-111000000ii−i−i00
χ5122-2-2-1222-21-2-221-12-2-2-1-12111-2-2-121-12-2-1-221-111-1-121-2-11-1-111000000-222i−2i00002i2i−2i−2i000000−2i−2i2i2i0000000000−ii1-2-12−i−iii11-1-1000000ii−i−i00
χ5222-2-2-1222-21-2-221-12-2-2-1-12111-2-2-121-12-2-1-221-111-1-121-2-11-1-111000000-22−2i2i0000−2i−2i2i2i0000002i2i−2i−2i0000000000i−i1-2-12ii−i−i11-1-1000000−i−iii00
χ532-22-222200-22-2-22-2-2-222222-2-22-2-2-22-200000022-2-200000000002-22-20000000000000000−i2i2−i2i2−i2i2−i2i22-22-20000000000000000000000−i2i2−i2i2−i2i2−i2i200
χ542-22-222200-22-2-22-2-2-222222-2-22-2-2-22-200000022-2-200000000002-22-20000000000000000i2−i2i2−i2i2−i2i2−i22-22-20000000000000000000000i2−i2i2−i2i2−i2i2−i200
χ552-22-222200-22-2-22-2-2-222222-2-22-2-2-22-200000022-2-20000000000-22-220000000000000000−i2i2−i2i2i2−i2i2−i2-22-220000000000000000000000−i2i2−i2i2i2−i2i2−i200
χ562-22-222200-22-2-22-2-2-222222-2-22-2-2-22-200000022-2-20000000000-22-220000000000000000i2−i2i2−i2−i2i2−i2i2-22-220000000000000000000000i2−i2i2−i2−i2i2−i2i200
χ572-2-22222002-22-2-2-2-22-2222-222-22-2-2-2-20000002-22-200000000002i−2i−2i2i0000000000000000−i2i2i2−i22−2−222i−2i−2i2i0000000000000000000000−i2i2i2−i22−2−2200
χ582-2-22222002-22-2-2-2-22-2222-222-22-2-2-2-20000002-22-200000000002i−2i−2i2i0000000000000000i2−i2−i2i2−222−22i−2i−2i2i0000000000000000000000i2−i2−i2i2−222−200
χ592-2-22222002-22-2-2-2-22-2222-222-22-2-2-2-20000002-22-20000000000−2i2i2i−2i0000000000000000−i2i2i2−i2−222−2−2i2i2i−2i0000000000000000000000−i2i2i2−i2−222−200
χ602-2-22222002-22-2-2-2-22-2222-222-22-2-2-2-20000002-22-20000000000−2i2i2i−2i0000000000000000i2−i2−i2i22−2−22−2i2i2i−2i0000000000000000000000i2−i2−i2i22−2−2200
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χ724444-2-2444-2-2-24-2-2-2441-2-211-2-2-2-2-2-2144-2-2-2-21111-2-2-2-2111111000000-4-40000000000000000000000000000000022220000-1-1-1-1000000000000
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χ8244-4-4-24-24-42-4-4-22-2422-21-222-1221-2-1-2-22-2-4421-1-111-2-12-2211-1-100000000−4i4i00002i2i−2i−2i000000000000000000002i−2i0000−i−iii0000000000000000
χ8344-4-4-24-2-442-4-4-22-2422-21-222-1221-2-1-22-224-4-21-1-11-121-22-2-1-1110000000000000023−23−232300000000000000000000000000−333−30000000000000000
χ8444-4-4-24-2-442-4-4-22-2422-21-222-1221-2-1-22-224-4-21-1-11-121-22-2-1-11100000000000000−232323−23000000000000000000000000003−3−330000000000000000
χ8544-4-4-2-244-422242-2-2-4-41-2-2-1-1222-2-2214-4-22-221-1-11-2-2221-111-1-10000004-400000000000000000000000000000000-2-222000011-1-1000000000000
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χ8744-4-4-2-24-4422242-2-2-4-41-2-2-1-1222-2-221-442-22-21-1-1122-2-2-11-1-1110000000000000000000000000000000000000000000000003-3-33000000000000
χ8844-4-4-2-24-4422242-2-2-4-41-2-2-1-1222-2-221-442-22-21-1-1122-2-2-11-1-111000000000000000000000000000000000000000000000000-333-3000000000000
χ894-44-444-200-44-424-4-42-24-2-24-42-2222-2-4000000-2-22200000000004-44-4000000000000000000000000-22-2200000000000000000000000000000000
χ904-44-444-200-44-424-4-42-24-2-24-42-2222-2-4000000-2-2220000000000-44-440000000000000000000000002-22-200000000000000000000000000000000
χ914-44-44-2400-4-22-44-42-44-24-2-22-4-22-4242000000-2-222000000000000000000000000000000−2i22i2−2i22i2000000000000000000000000000000i2−i2i2−i2000000
χ924-44-44-2400-4-22-44-42-44-24-2-22-4-22-4242000000-2-2220000000000000000000000000000002i2−2i22i2−2i2000000000000000000000000000000−i2i2−i2i2000000
χ934-44-4-2440024-4-4-22-4-44-2-24-2224-42-4-22000000-2-2220000000000000000000000000000000000−2i22i2−2i22i2000000000000000000000000000000i2−i2i2−i200
χ944-44-4-2440024-4-4-22-4-44-2-24-2224-42-4-22000000-2-22200000000000000000000000000000000002i2−2i22i2−2i2000000000000000000000000000000−i2i2−i2i200
χ954-4-4444-2004-442-4-4-4-224-2-2-44-22-2222-4000000-22-2200000000004i−4i−4i4i000000000000000000000000−2i2i2i−2i00000000000000000000000000000000
χ964-4-4444-2004-442-4-4-4-224-2-2-44-22-2222-4000000-22-220000000000−4i4i4i−4i0000000000000000000000002i−2i−2i2i00000000000000000000000000000000
χ974-4-444-240042-2-4-4-424-4-24-22-242-2-42-42000000-22-22000000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000000i2−i2−i2i2000000
χ984-4-444-240042-2-4-4-424-4-24-22-242-2-42-42000000-22-220000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000000−i2i2i2−i2000000
χ994-4-44-24400-2-44-422-44-4-2-242-2-2-442-422000000-22-22000000000000000000000000000000000022−22−2222000000000000000000000000000000−222−200
χ1004-4-44-24400-2-44-422-44-4-2-242-2-2-442-422000000-22-220000000000000000000000000000000000−222222−220000000000000000000000000000002−2−2200
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
χ10388-8-8-4-4-48-8444-44-4-444222-2-2-2-2-222-22-44-44-44-111-122-2-22-2-1-1110000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-4-88444-44-4-444222-2-2-2-2-222-224-44-44-4-111-1-2-222-2211-1-10000000000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-400-8-4448-844-4-4-42-4442-24-2-4400000022-2-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-48-40048-84-44-84-4-42-4-44-2-44-242400000022-2-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-48004-44-8-444-882-4-42-24-4444-4-200000022-2-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4004-444-4444-42222-2-22-2-2-22-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4004-444-4444-42222-2-22-2-2-22-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000000000000000000
χ1108-8-888-4-40084-44-8-84-44-4-424-4-4-224-2440000002-22-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-400-4-88444-8-44-42-44-424-4-24-240000002-22-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-4800-44-4-84448-82-4-4-22-44-4444-20000002-22-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-400-44-44444-44222-222-22-2-2-2-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-400-44-44444-44222-222-22-2-2-2-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000000000000000

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