Finite Group Databasebeta

← Group #13155674

Character table — Group #13155674

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212181818181818181824242424242424242424242436363636363672727272108108
order12223334466666666633366666666612121212121212121212366612121212121212124444881212121212121212242424242424242424242424242424244444121212121212121212121212121212122244121266121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-11111
χ51111111111111111111111111111111111111111111111111111-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111
χ71111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
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
χ911-1-11111-1-1-1-1111-1-1-1111-1-1-1-1-111-11-11-1-1-1-111111-1-111-11-111-1-11-1i−i1-111-1-1ii−i−i11111111-1-1-1-1-1-1-1-1i−ii−iii−i−i1-1i−iii−i−i11-1-11-1i−ii−i1-1i−ii−i
χ1011-1-11111-1-1-1-1111-1-1-1111-1-1-1-1-111-11-11-1-1-1-111111-1-111-11-111-1-11-1i−i-1111-1-1ii−i−i-1-1-1-1-1-1-1-111111111i−ii−iii−i−i1-1i−iii−i−i11-1-1-11−iii−i-11−ii−ii
χ1111-1-11111-1-1-1-1111-1-1-1111-1-1-1-1-111-11-11-1-1-1-111111-1-111-11-111-1-11-1−ii1-111-1-1−i−iii11111111-1-1-1-1-1-1-1-1−ii−ii−i−iii1-1−ii−i−iii11-1-11-1−ii−ii1-1−ii−ii
χ1211-1-11111-1-1-1-1111-1-1-1111-1-1-1-1-111-11-11-1-1-1-111111-1-111-11-111-1-11-1−ii-1111-1-1−i−iii-1-1-1-1-1-1-1-111111111−ii−ii−i−iii1-1−ii−i−iii11-1-1-11i−i−ii-11i−ii−i
χ1311-1-11111-1-1-1-1111-1-1-1111-1-1-1-1-111-11-11-1-1-1-111111-1-111-11-111-1-1-11i−i1-1-1-111ii−i−i11111111-1-1-1-1-1-1-1-1−ii−ii−i−iii-11i−iii−i−i-1-111-11i−i−ii-11i−i−ii
χ1411-1-11111-1-1-1-1111-1-1-1111-1-1-1-1-111-11-11-1-1-1-111111-1-111-11-111-1-1-11i−i-11-1-111ii−i−i-1-1-1-1-1-1-1-111111111−ii−ii−i−iii-11i−iii−i−i-1-1111-1−ii−ii1-1−iii−i
χ1511-1-11111-1-1-1-1111-1-1-1111-1-1-1-1-111-11-11-1-1-1-111111-1-111-11-111-1-1-11−ii1-1-1-111−i−iii11111111-1-1-1-1-1-1-1-1i−ii−iii−i−i-11−ii−i−iii-1-111-11−iii−i-11−iii−i
χ1611-1-11111-1-1-1-1111-1-1-1111-1-1-1-1-111-11-11-1-1-1-111111-1-111-11-111-1-1-11−ii-11-1-111−i−iii-1-1-1-1-1-1-1-111111111i−ii−iii−i−i-11−ii−i−iii-1-1111-1i−ii−i1-1i−i−ii
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000022-2-222220000000000000000-2-2000000
χ182222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000-2-222-2-2-2-2000000000000000022000000
χ19222222-1222-1-122-12222-1-12-1-1-1-12-12-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-12200222222000022-1-1-1-1-1-122-1-1-1-1-1-100000000-1-1000000-1-1-1-1220000-1-10000
χ20222222-1222-1-122-12222-1-12-1-1-1-12-12-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-12200-2-222220000-2-2111111-2-211111100000000-1-1000000-1-1-1-1-2-20000110000
χ21222222-1222-1-122-12222-1-12-1-1-1-12-12-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-1-2-20022-2-2-2-2000022-1-1-1-1-1-122-1-1-1-1-1-100000000110000001111-2-20000110000
χ22222222-1222-1-122-12222-1-12-1-1-1-12-12-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2-2-2-2-2-20000-2-2111111-2-211111100000000110000001111220000-1-10000
χ2322222-12222222-12-1-12-12-1-122-1-1-12-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1222200-1-1-1-1-1-1-1-100000000000000002222-1-1-1-12222-1-1-1-1-1-1-1-10000-1-1000000
χ2422222-12222222-12-1-12-12-1-122-1-1-12-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122-2-200-1-1-1-111110000000000000000-2-2-2-2111122-2-21111-1-1-1-1000011000000
χ2522222-12222222-12-1-12-12-1-122-1-1-12-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-222001111-1-1-1-10000000000000000-2-2-2-21111-2-222-1-1-1-11111000011000000
χ2622222-12222222-12-1-12-12-1-122-1-1-12-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2001111111100000000000000002222-1-1-1-1-2-2-2-2111111110000-1-1000000
χ2722222-12-2-22222-12-1-12-12-1-122-1-1-12-1-1-211-2-2-2-2-2-2-2-1-1-1-111111111000000−i3i3−i3i3−i3i3−i3i3000000000000000022-2-2-1-1-1-10000−i3i3−i3i3−i3i3−i3i3000011000000
χ2822222-12-2-22222-12-1-12-12-1-122-1-1-12-1-1-211-2-2-2-2-2-2-2-1-1-1-111111111000000−i3i3−i3i3i3−i3i3−i30000000000000000-2-22211110000i3−i3i3−i3−i3i3−i3i30000-1-1000000
χ2922222-12-2-22222-12-1-12-12-1-122-1-1-12-1-1-211-2-2-2-2-2-2-2-1-1-1-111111111000000i3−i3i3−i3−i3i3−i3i30000000000000000-2-22211110000−i3i3−i3i3i3−i3i3−i30000-1-1000000
χ3022222-12-2-22222-12-1-12-12-1-122-1-1-12-1-1-211-2-2-2-2-2-2-2-1-1-1-111111111000000i3−i3i3−i3i3−i3i3−i3000000000000000022-2-2-1-1-1-10000i3−i3i3−i3i3−i3i3−i3000011000000
χ312222-12222-122-12222-1-1-12-1-1-122-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100222200002222-1-122-1-1-1-1-1-122-1-1-1-10000000000-1-1-1-1-1-1000000220000-1-100
χ322222-12222-122-12222-1-1-12-1-1-122-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-10022-2-20000222211-2-2111111-2-211110000000000-1-1-1-1-1-1000000-2-200001100
χ332222-12222-122-12222-1-1-12-1-1-122-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100-2-2220000-2-2-2-2-1-122-1-1-1-1-1-122-1-1-1-10000000000111111000000-2-200001100
χ342222-12222-122-12222-1-1-12-1-1-122-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2-20000-2-2-2-211-2-2111111-2-211110000000000111111000000220000-1-100
χ3522-2-2222-22-2-2-2222-2-2-2222-2-2-2-2-222-222-22222-2-2-2-22-2-22-22-22-2-2220000000000000000000000000000002i−2i−2i2i2i2i−2i−2i0000000000000000−2i2i000000
χ3622-2-2222-22-2-2-2222-2-2-2222-2-2-2-2-222-222-22222-2-2-2-22-2-22-22-22-2-222000000000000000000000000000000−2i2i2i−2i−2i−2i2i2i00000000000000002i−2i000000
χ3722-2-222-12-2-21122-1-2-2-22-1-1-211112-1-2-1-22-21112-1-1-1-111-12-2-11-1-1112-2002-222-2-2000022-1-1-1-1-1-1-2-211111100000000-11000000-1-1112-20000-110000
χ3822-2-222-12-2-21122-1-2-2-22-1-1-211112-1-2-1-22-21112-1-1-1-111-12-2-11-1-1112-200-2222-2-20000-2-211111122-1-1-1-1-1-100000000-11000000-1-111-2200001-10000
χ3922-2-222-12-2-21122-1-2-2-22-1-1-211112-1-2-1-22-21112-1-1-1-111-12-2-11-1-111-22002-2-2-222000022-1-1-1-1-1-1-2-2111111000000001-100000011-1-1-2200001-10000
χ4022-2-222-12-2-21122-1-2-2-22-1-1-211112-1-2-1-22-21112-1-1-1-111-12-2-11-1-111-2200-22-2-2220000-2-211111122-1-1-1-1-1-1000000001-100000011-1-12-20000-110000
χ4122-2-22-122-2-2-2-22-1211-2-12-11-2-211-121-1-2-11-2-2-22222-111-1-11-11-1-1112-22i−2i00-1-111−i−iii00000000000000002i−2i2i−2i−i−iii2-22i−2i−i−iii-1-1110000−ii000000
χ4222-2-22-122-2-2-2-22-1211-2-12-11-2-211-121-1-2-11-2-2-22222-111-1-11-11-1-1112-2−2i2i00-1-111ii−i−i0000000000000000−2i2i−2i2iii−i−i2-2−2i2iii−i−i-1-1110000i−i000000
χ4322-2-22-122-2-2-2-22-1211-2-12-11-2-211-121-1-2-11-2-2-22222-111-1-11-11-1-111-222i−2i0011-1-1−i−iii0000000000000000−2i2i−2i2iii−i−i-222i−2i−i−iii11-1-10000i−i000000
χ4422-2-22-122-2-2-2-22-1211-2-12-11-2-211-121-1-2-11-2-2-22222-111-1-11-11-1-111-22−2i2i0011-1-1ii−i−i00000000000000002i−2i2i−2i−i−iii-22−2i2iii−i−i11-1-10000−ii000000
χ4522-2-22-12-22-2-2-22-1211-2-12-11-2-211-121-121-1222-2-2-2-2-111-11-11-111-1-1000000−i3i3i3−i33−3−3300000000000000002i−2i−2i2i−i−iii00003−3−33−i3i3i3−i30000i−i000000
χ4622-2-22-12-22-2-2-22-1211-2-12-11-2-211-121-121-1222-2-2-2-2-111-11-11-111-1-1000000−i3i3i3−i3−333−30000000000000000−2i2i2i−2iii−i−i0000−333−3−i3i3i3−i30000−ii000000
χ4722-2-22-12-22-2-2-22-1211-2-12-11-2-211-121-121-1222-2-2-2-2-111-11-11-111-1-1000000i3−i3−i3i33−3−330000000000000000−2i2i2i−2iii−i−i00003−3−33i3−i3−i3i30000−ii000000
χ4822-2-22-12-22-2-2-22-1211-2-12-11-2-211-121-121-1222-2-2-2-2-111-11-11-111-1-1000000i3−i3−i3i3−333−300000000000000002i−2i−2i2i−i−iii0000−333−3i3−i3−i3i30000i−i000000
χ4922-2-2-1222-21-2-2-122-2-21-1-12111-2-2-1-11212-2-211-12-1-1-111-1-112-2-1-111002i−2i2-200002i2i−2i−2i-1-122-1-1-1-111-2-211110000000000−ii−i−iii0000002i−2i0000−ii00
χ5022-2-2-1222-21-2-2-122-2-21-1-12111-2-2-1-11212-2-211-12-1-1-111-1-112-2-1-111002i−2i-2200002i2i−2i−2i11-2-21111-1-122-1-1-1-10000000000−ii−i−iii000000−2i2i0000i−i00
χ5122-2-2-1222-21-2-2-122-2-21-1-12111-2-2-1-11212-2-211-12-1-1-111-1-112-2-1-11100−2i2i2-20000−2i−2i2i2i-1-122-1-1-1-111-2-211110000000000i−iii−i−i000000−2i2i0000i−i00
χ5222-2-2-1222-21-2-2-122-2-21-1-12111-2-2-1-11212-2-211-12-1-1-111-1-112-2-1-11100−2i2i-220000−2i−2i2i2i11-2-21111-1-122-1-1-1-10000000000i−iii−i−i0000002i−2i0000−ii00
χ53444444-2-4-44-2-244-24444-2-24-2-2-2-24-24-2-4-4-4222-4222-2-2-2-2-4-422222200000000000000000000000000000000000000000000000000000000000000
χ5444444-2-2444-2-24-2-2-2-24-2-21-2-2-211-2-2-214-2-2-2-2-24-2-2-21111-2-2111111440000-2-2-2-20000000000000000000000000000-2-20000001111000000000000
χ5544444-2-2444-2-24-2-2-2-24-2-21-2-2-211-2-2-214-2-2-2-2-24-2-2-21111-2-2111111-4-400002222000000000000000000000000000022000000-1-1-1-1000000000000
χ5644444-2-2-4-44-2-24-2-2-2-24-2-21-2-2-211-2-2-21-422222-4222111122-1-1-1-1-1-1000000−2i32i3−2i32i3000000000000000000000000000000000000i3−i3i3−i3000000000000
χ5744444-2-2-4-44-2-24-2-2-2-24-2-21-2-2-211-2-2-21-422222-4222111122-1-1-1-1-1-10000002i3−2i32i3−2i3000000000000000000000000000000000000−i3i3−i3i3000000000000
χ584444-244-4-4-244-24444-2-2-24-2-2-244-2-2-242-4-4-4222-422-2-2-2-222-4-4222200000000000000000000000000000000000000000000000000000000000000
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χ604444-24-244-2-2-2-24-244-2-21-2-211-2-2-21-2-2-244-211-2-2111111-2-2-2-211110000-4-4000000002222-1-1-1-12222-1-1-1-100000000000000000000000000000000
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χ6844-4-44-2-24-4-4224-2-222-4-2-21222-1-1-2-221-4-222224-2-2-21-1-11-221-111-1-14-40000-2-2220000000000000000000000000000-2200000011-1-1000000000000
χ6944-4-44-2-24-4-4224-2-222-4-2-21222-1-1-2-221-4-222224-2-2-21-1-11-221-111-1-1-44000022-2-200000000000000000000000000002-2000000-1-111000000000000
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χ7144-4-44-2-2-44-4224-2-222-4-2-21222-1-1-2-22142-2-2-2-2-42221-1-112-2-11-1-1110000002i3−2i3−2i32i3000000000000000000000000000000000000−i3i3i3−i3000000000000
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χ7444-4-4-24-24-4222-24-2-4-42-21-22-1-122-212-224-42-1-1-2-2111-1-11-22-2211-1-10000-44000000002222-1-1-1-1-2-2-2-2111100000000000000000000000000000000
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χ7844-4-4-2-244-42-4-4-2-242221-2-2-122221-2-1-22-22-422-24-2-21-1-111-1-2211-1-100−4i4i0000002i2i−2i−2i000000000000000000000000002i−2i−i−iii0000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.