Finite Group Databasebeta

← Group #13156524

Character table — Group #13156524

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212181818182424242424242424242424242424242424243636363654545454727272727272
order1222333446666666663336666666661212121212121212121288883666121212121212121224242424242424242424242424242424888844121212121212121212121212121212122424242444444412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-1-1
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χ12222222-12222-1222-1-122-1-12-1-1-1-12-12-12-12-1-1-12-1-122222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-200000-2-21100001111000000000-21100
χ13222222-12222-1222-1-122-1-12-1-1-1-12-12-12-12-1-1-12-1-12-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-2111111111111000020000022-1-10000-1-1-1-1000000000-21100
χ14222222-12222-1222-1-122-1-12-1-1-1-12-12-12-12-1-1-12-1-12-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-21111111111110000-200000-2-211000011110000000002-1-100
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χ874-4-4444-200-4-4244-42-2-44-2-2-42-22-2-42420000000000−2i22i22i2−2i2-22-2200000000−2i22i22i2−2i2i2−i2−i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000000000000000
χ884-4-4444-200-4-4244-42-2-44-2-2-42-22-2-424200000000002i2−2i2−2i22i2-22-22000000002i2−2i2−2i22i2−i2i2i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000000000000000
χ894-4-444-2400-42-44-2-4-442-24-22-442-222-2-40000000000−2i22i22i2−2i2-22-2200000000i2−i2−i2i2−2i22i22i2−2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000000000000000
χ904-4-444-2400-42-44-2-4-442-24-22-442-222-2-400000000002i2−2i2−2i22i2-22-2200000000−i2i2i2−i22i2−2i2−2i22i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000000000000000
χ914-4-444-2-200-4224-2-42-22-2-2122-2-112-1-220003i−3i00−3i3i0−2i22i22i2−2i21-11-10000−3i3i3i−3ii2−i2−i2i2i2−i2−i2i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23000000000000000000000000000000000000
χ924-4-444-2-200-4224-2-42-22-2-2122-2-112-1-220003i−3i00−3i3i02i2−2i2−2i22i21-11-10000−3i3i3i−3i−i2i2i2−i2−i2i2i2−i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23000000000000000000000000000000000000
χ934-4-444-2-200-4224-2-42-22-2-2122-2-112-1-22000−3i3i003i−3i0−2i22i22i2−2i21-11-100003i−3i−3i3ii2−i2−i2i2i2−i2−i2i2−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23000000000000000000000000000000000000
χ944-4-444-2-200-4224-2-42-22-2-2122-2-112-1-22000−3i3i003i−3i02i2−2i2−2i22i21-11-100003i−3i−3i3i−i2i2i2−i2−i2i2i2−i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23000000000000000000000000000000000000
χ954-4-44-244002-4-4-242-44-4-2-2422-2-442-4-2200000000000000-22-22000000000000000000000000−2i22i22i2−2i2000000000000000000i2−i2−i2i20000000000
χ964-4-44-244002-4-4-242-44-4-2-2422-2-442-4-2200000000000000-22-220000000000000000000000002i2−2i2−2i22i2000000000000000000−i2i2i2−i20000000000
χ978888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-422-4-422-40000-1-1-1-12222-1-1-1-10000000000000000000000000000000000000000000000000000
χ988888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444-2-244-2-240000-1-1-1-1-2-2-2-211110000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-48-844444-4-44-4222-2-2-2-2-222-22-444-2-2-4-42240000-111-12-22-2-1-1110000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-8844444-4-44-4222-2-2-2-2-222-224-4-42244-2-2-40000-111-1-22-2211-1-10000000000000000000000000000000000000000000000000000
χ1018-88-8-48-400-48-44-8444-8-42-4-42-2-44444-20000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4800-4-48444-8-842-4-42-44-44-24-240000000000000022-2-2000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-400-4-4-444444422222-22-2-2-2-2-20006i−6i006i−6i00000-1-1110000−3i3i−3i3i0000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-400-4-4-444444422222-22-2-2-2-2-2000−6i6i00−6i6i00000-1-11100003i−3i3i−3i0000000000000000000000000000000000000000000000000000
χ1058-8-88-48-4004-84-4844-4-8-42-44-224-444-4-2000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-480044-8-4-44-8842-4-4-24-44-4-2424000000000000002-22-2000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-400444-4-444-44222-2-22-22-2-22-20006i−6i00−6i6i00000-11-1100003i−3i−3i3i0000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-400444-4-444-44222-2-22-22-2-22-2000−6i6i006i−6i00000-11-110000−3i3i3i−3i0000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.