Finite Group Databasebeta

← Group #13155756

Character table — Group #13155756

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212181818181818181824242424242424242424242436363636363672727272108108
order124423334666121212121212333666666661212121212121212121212366666121212121212244466881212121212121212121212121212121212122424242488882424242466612121224242424242424882424612242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-111
χ51111111111111111111111111111111111111111111111111111-1-111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ911-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-111111-1-11-1i−i11i−i-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−iii−i−i111-1-1-1i−iii−i−i1-1i−ii−i1-1i−i1-1
χ1011-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-111111-1-11-1i−i11−ii-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii−i−iii111-1-1-1−ii−i−iii-11i−i−ii-11i−i-11
χ1111-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-111111-1-11-1−ii11i−i-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−iii−i−i111-1-1-1i−iii−i−i-11−iii−i-11−ii-11
χ1211-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-111111-1-11-1−ii11−ii-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii−i−iii111-1-1-1−ii−i−iii1-1−ii−ii1-1−ii1-1
χ1311-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-111111-1-1-11i−i-1-1i−i11iiiiiiii−i−i−i−i−i−i−i−iii−i−i−i−iii−i−iii-1-1-1111i−iii−i−i1-1−ii−ii1-1−ii-11
χ1411-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-111111-1-1-11i−i-1-1−ii11iiiiiiii−i−i−i−i−i−i−i−i−i−iiiii−i−iii−i−i-1-1-1111−ii−i−iii-11−iii−i-11−ii1-1
χ1511-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-111111-1-1-11−ii-1-1i−i11−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−iii−i−iii-1-1-1111i−iii−i−i-11i−i−ii-11i−i1-1
χ1611-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-111111-1-1-11−ii-1-1−ii11−i−i−i−i−i−i−i−iiiiiiiii−i−iiiii−i−iii−i−i-1-1-1111−ii−i−iii1-1i−ii−i1-1i−i-11
χ172222222-1222-1-1-12222-1-122-1-12-1-1-1222-1-1-1-1-122-1-1-1-12-1-1-1-12-1-1-1-1002200220022-1-1-1-1-1-122-1-1-1-1-1-1222200000000000000-1-1-1-1-1-1220000-1-10000
χ182222222-1222-1-1-12222-1-122-1-12-1-1-1222-1-1-1-1-122-1-1-1-12-1-1-1-12-1-1-1-1002200-2-20022-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-200000000000000111111-2-20000110000
χ192222222-1222-1-1-12222-1-122-1-12-1-1-1222-1-1-1-1-122-1-1-1-12-1-1-1-12-1-1-1-100-2-2002200-2-2111111-2-2111111222200000000000000-1-1-1-1-1-1-2-20000110000
χ202222222-1222-1-1-12222-1-122-1-12-1-1-1222-1-1-1-1-122-1-1-1-12-1-1-1-12-1-1-1-100-2-200-2-200-2-2111111-2-2111111-2-2-2-200000000000000111111220000-1-10000
χ21222222-1222-122222-1-12-1-1-12-12222-12-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12200-1-122-1-10000000000000000-1-1-1-12222-1-1-1-12-1-12-1-122-1-1-1-10000-1-1000000
χ22222222-1222-122222-1-12-1-1-12-12222-12-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12200-1-1-2-2-1-100000000000000001111-2-2-2-211112-1-12-1-1-2-21111000011000000
χ23222222-1222-122222-1-12-1-1-12-12222-12-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2001122110000000000000000-1-1-1-1-2-2-2-21111-211-21122-1-1-1-1000011000000
χ24222222-1222-122222-1-12-1-1-12-12222-12-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20011-2-211000000000000000011112222-1-1-1-1-211-211-2-211110000-1-1000000
χ2522222-1222-12222-1-122-12-12-12-12-1-1-1-122-1-1-1-1-1-122-12-1-1-1-12-1-1-1-1-12222220022-1-122-1-1-1-1-1-122-1-1-1-1000000000000-1-1-1-1-1-100000000220000-1-100
χ2622222-1222-12222-1-122-12-12-12-12-1-1-1-122-1-1-1-1-1-122-12-1-1-1-12-1-1-1-1-122-2-222002211-2-2111111-2-21111000000000000-1-1-1-1-1-100000000-2-200001100
χ2722222-1222-12222-1-122-12-12-12-12-1-1-1-122-1-1-1-1-1-122-12-1-1-1-12-1-1-1-1-1-2-222-2-200-2-2-1-122-1-1-1-1-1-122-1-1-1-100000000000011111100000000-2-200001100
χ2822222-1222-12222-1-122-12-12-12-12-1-1-1-122-1-1-1-1-1-122-12-1-1-1-12-1-1-1-1-1-2-2-2-2-2-200-2-211-2-2111111-2-2111100000000000011111100000000220000-1-100
χ292222-2222-2222222222222-222-2-2-2-22-2-2-2-2-22222222-2-2-2-22-2-2-2-2220000000000000000000000000000002-22-222220000000000000000-2-2000000
χ302222-2222-2222222222222-222-2-2-2-22-2-2-2-2-22222222-2-2-2-22-2-2-2-222000000000000000000000000000000-22-22-2-2-2-2000000000000000022000000
χ312222-22-12-22-122222-1-12-1-112-1-2-2-2-2-1-21-2-2-222-1-1-1-1-11111-11111-1-10000−i3i300−i3i30000000000000000−i3i3−i3i32-22-2-1-1-1-10−i3i30−i3i300−i3i3−i3i3000011000000
χ322222-22-12-22-122222-1-12-1-112-1-2-2-2-2-1-21-2-2-222-1-1-1-1-11111-11111-1-10000−i3i300−i3i30000000000000000i3−i3i3−i3-22-2211110−i3i30−i3i300i3−i3i3−i30000-1-1000000
χ332222-22-12-22-122222-1-12-1-112-1-2-2-2-2-1-21-2-2-222-1-1-1-1-11111-11111-1-10000i3−i300i3−i30000000000000000−i3i3−i3i3-22-2211110i3−i30i3−i300−i3i3−i3i30000-1-1000000
χ342222-22-12-22-122222-1-12-1-112-1-2-2-2-2-1-21-2-2-222-1-1-1-1-11111-11111-1-10000i3−i300i3−i30000000000000000i3−i3i3−i32-22-2-1-1-1-10i3−i30i3−i300i3−i3i3−i3000011000000
χ3522-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000002i−2i−2i2i2i2i−2i−2i0000000000000000−2i2i000000
χ3622-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000−2i2i2i−2i−2i−2i2i2i00000000000000002i−2i000000
χ3722-2-222-12-22-12-2-2-2-2112-1-1-12-12222-1-21-2-2-2-2-21111-1-1-1-1-1-11111110000−i3i300i3−i300000000000000003−3−332i−2i−2i2i−i−iii0−i3i30i3−i3003−3−330000i−i000000
χ3822-2-222-12-22-12-2-2-2-2112-1-1-12-12222-1-21-2-2-2-2-21111-1-1-1-1-1-11111110000−i3i300i3−i30000000000000000−333−3−2i2i2i−2iii−i−i0−i3i30i3−i300−333−30000−ii000000
χ3922-2-222-12-22-12-2-2-2-2112-1-1-12-12222-1-21-2-2-2-2-21111-1-1-1-1-1-11111110000i3−i300−i3i300000000000000003−3−33−2i2i2i−2iii−i−i0i3−i30−i3i3003−3−330000−ii000000
χ4022-2-222-12-22-12-2-2-2-2112-1-1-12-12222-1-21-2-2-2-2-21111-1-1-1-1-1-11111110000i3−i300−i3i30000000000000000−333−32i−2i−2i2i−i−iii0i3−i30−i3i300−333−30000i−i000000
χ4122-2-2-222-1222-111-2-2-2-2-1-12-2-1-1-2111222-1-1-111-2-211-11-211-1-12-1-111002i−2i002i−2i002i2i−i−i−i−i−i−i−2i−2iiiiiii2i2i−2i−2i00000000000000−ii−i−iii2-20000-110000
χ4222-2-2-222-1222-111-2-2-2-2-1-12-2-1-1-2111222-1-1-111-2-211-11-211-1-12-1-111002i−2i00−2i2i002i2i−i−i−i−i−i−i−2i−2iiiiiii−2i−2i2i2i00000000000000i−iii−i−i-2200001-10000
χ4322-2-2-222-1222-111-2-2-2-2-1-12-2-1-1-2111222-1-1-111-2-211-11-211-1-12-1-11100−2i2i002i−2i00−2i−2iiiiiii2i2i−i−i−i−i−i−i2i2i−2i−2i00000000000000−ii−i−iii-2200001-10000
χ4422-2-2-222-1222-111-2-2-2-2-1-12-2-1-1-2111222-1-1-111-2-211-11-211-1-12-1-11100−2i2i00−2i2i00−2i−2iiiiiii2i2i−i−i−i−i−i−i−2i−2i2i2i00000000000000i−iii−i−i2-20000-110000
χ4522-2-2-22-1222-12-2-2-2-2112-1-112-1-2-2-2-2-12-1222-2-21111-11111-1-1-1-1-1112-200-1-12i−2i110000000000000000−i−iii2i2i−2i−2i−i−iii2-1-1-2112i−2i−i−iii0000−ii000000
χ4622-2-2-22-1222-12-2-2-2-2112-1-112-1-2-2-2-2-12-1222-2-21111-11111-1-1-1-1-1112-200-1-1−2i2i110000000000000000ii−i−i−2i−2i2i2iii−i−i2-1-1-211−2i2iii−i−i0000i−i000000
χ4722-2-2-22-1222-12-2-2-2-2112-1-112-1-2-2-2-2-12-1222-2-21111-11111-1-1-1-1-111-2200112i−2i-1-10000000000000000−i−iii−2i−2i2i2iii−i−i-2112-1-12i−2i−i−iii0000i−i000000
χ4822-2-2-22-1222-12-2-2-2-2112-1-112-1-2-2-2-2-12-1222-2-21111-11111-1-1-1-1-111-220011−2i2i-1-10000000000000000ii−i−i2i2i−2i−2i−i−iii-2112-1-1−2i2iii−i−i0000−ii000000
χ4922-2-2-2-1222-122-2-211-2-2-12-1-2-121-211-1-122-1-11111-2-2-1-2111-12-1-1-1112-22i−2i2200-2-2−i−i2i2i−i−i−i−iii−2i−2iiiii000000000000-1-1-1111000000002i−2i0000−ii00
χ5022-2-2-2-1222-122-2-211-2-2-12-1-2-121-211-1-122-1-11111-2-2-1-2111-12-1-1-1112-2−2i2i2200-2-2ii−2i−2iiiii−i−i2i2i−i−i−i−i000000000000-1-1-111100000000−2i2i0000i−i00
χ5122-2-2-2-1222-122-2-211-2-2-12-1-2-121-211-1-122-1-11111-2-2-1-2111-12-1-1-111-222i−2i-2-20022−i−i2i2i−i−i−i−iii−2i−2iiiii000000000000111-1-1-100000000−2i2i0000i−i00
χ5222-2-2-2-1222-122-2-211-2-2-12-1-2-121-211-1-122-1-11111-2-2-1-2111-12-1-1-111-22−2i2i-2-20022ii−2i−2iiiii−i−i2i2i−i−i−i−i000000000000111-1-1-1000000002i−2i0000−ii00
χ53444444-2-244-2-2-2-244-2-2-21-2-2-214-2-2-2-24-2-2-2-2-2-2-2-21111-21111-2111100000044000000000000000000-2-2-2-200000000000000-2-21111000000000000
χ54444444-2-244-2-2-2-244-2-2-21-2-2-214-2-2-2-24-2-2-2-2-2-2-2-21111-21111-21111000000-4-400000000000000000022220000000000000022-1-1-1-1000000000000
χ5544444-24-24-24-2-2-2-2-2441-2-241-2-2-211-2-24-21111-2-2-2-21-2-2111-2-211110044000000-2-2-2-21111-2-2-2-21111000000000000000000000000000000000000
χ5644444-24-24-24-2-2-2-2-2441-2-241-2-2-211-2-24-21111-2-2-2-21-2-2111-2-2111100-4-40000002222-1-1-1-12222-1-1-1-1000000000000000000000000000000000000
χ5744444-2-244-2-2444-2-2-2-2-2-21-2-2-2-24-2-21-2-24-2-2-2-211-2-21-21111-2111114400-2-200-2-20000000000000000000000000000-211-211000000000000000000
χ5844444-2-244-2-2444-2-2-2-2-2-21-2-2-2-24-2-21-2-24-2-2-2-211-2-21-21111-211111-4-40022002200000000000000000000000000002-1-12-1-1000000000000000000
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χ614444-44-2-2-44-2-2-2-244-2-2-21-22-21-4222-2-42222-2-2-2-2111-12-1-11-12-1-111000000000000000000000000002i3−2i32i3−2i30000000000000000−i3i3−i3i3000000000000
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χ654444-4-2-24-4-2-2444-2-2-2-2-2-212-2-22-422122-422-2-211-2-212-1-1-112-1-1-1110000−2i32i300−2i32i300000000000000000000000000000i3−i30i3−i3000000000000000000
χ664444-4-2-24-4-2-2444-2-2-2-2-2-212-2-22-422122-422-2-211-2-212-1-1-112-1-1-11100002i3−2i3002i3−2i300000000000000000000000000000−i3i30−i3i3000000000000000000
χ6744-4-4444-2-444-222-4-4-4-4-2-244-2-24-2-2-24-4-422222-4-422-2-24-2-2-22-4222200000000000000000000000000000000000000000000000000000000000000
χ6844-4-444-2-2-44-2-222-4-422-21-2-2-214-2-2-2-2-422222222-1-111-2111-12-1-1-1-10000000000000000000000000023−23−23230000000000000000−333−3000000000000
χ6944-4-444-2-2-44-2-222-4-422-21-2-2-214-2-2-2-2-422222222-1-111-2111-12-1-1-1-100000000000000000000000000−232323−2300000000000000003−3−33000000000000
χ7044-4-44-244-4-244-4-422-4-4-24-24-24-24-2-2-22-4-4222222-4-4-24-2-2-2-2-42222200000000000000000000000000000000000000000000000000000000000000
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χ7244-4-44-24-2-4-24-22222-4-41-2-241-2-2-211-22-42-1-1-1-122221-2-211122-1-1-1-100000000000000-3-333000033-3-3000000000000000000000000000000000000
χ7344-4-44-2-24-4-2-24-4-42222-2-21-2-2-2-24-2-2122-42222-1-1221-211112-1-1-1-1-10000−2i32i3002i3−2i300000000000000000000000000000i3−i30−i3i3000000000000000000
χ7444-4-44-2-24-4-2-24-4-42222-2-21-2-2-2-24-2-2122-42222-1-1221-211112-1-1-1-1-100002i3−2i300−2i32i300000000000000000000000000000−i3i30i3−i3000000000000000000
χ7544-4-4-44-2-244-2-222-4-422-21-22-21-4222-24-2-2-2-22222-1-11-12-1-111-211-1-10000004i−4i000000000000000000−2i−2i2i2i00000000000000−2i2iii−i−i000000000000
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χ7744-4-4-4-24-24-24-22222-4-41-2-2-41-222-1-1-2-24-211-1-12222122-1-11-2-211-1-1004i−4i000000−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.