Finite Group Databasebeta

← Group #10695260

Character table — Group #10695260

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order12222222222234444666666644666688888888121212124444444444441212121212121212121224242424242424244444888888884412121212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ911111111-1-1-1-11-1-1-1-1111111111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-1-1-1ii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-111iiii−i−i−i−i1-111-1-1ii−i−i1-1
χ1011111111-1-1-1-11-1-1-1-1111111111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-1-1-1−i−iii11−i−i−i−iiiiiiiii−i−i−i−i-1-111iiii−i−i−i−i-11-1-111−i−iii-11
χ1111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-11111ii−i−i11iiii−i−i−i−iiiii−i−i−i−i11-1-1−i−i−i−iiiii1-111-1-1−i−iii-11
χ1211111111-1-1-1-11-1-1-1-1111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-11111−i−iii11−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−i−i−iiiii-11-1-111ii−i−i1-1
χ1311111111-1-1-1-11-1-1-1-1111111111-1-1-1-1−i−i−i−iiiii-1-1-1-11111-1-1-1-1ii−i−i11iiii−i−i−i−i−i−i−i−iiiii-1-111−i−i−i−iiiii-11-1-111ii−i−i-11
χ1411111111-1-1-1-11-1-1-1-1111111111-1-1-1-1−i−i−i−iiiii-1-1-1-11111-1-1-1-1−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-111−i−i−i−iiiii1-111-1-1−i−iii1-1
χ1511111111-1-1-1-11-1-1-1-1111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-11111ii−i−i11iiii−i−i−i−i−i−i−i−iiiii11-1-1iiii−i−i−i−i-11-1-111−i−iii1-1
χ1611111111-1-1-1-11-1-1-1-1111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-11111−i−iii11−i−i−i−iiiii−i−i−i−iiiii11-1-1iiii−i−i−i−i1-111-1-1ii−i−i-11
χ172222222222222-2-2-2-22222222-2-2222200000000-2-2-2-22222-2-2-2-20000-2-2000000000000000022-2-200000000000000000000
χ182222222222222-2-2-2-22222222-2-2222200000000-2-2-2-2-2-2-2-222220000-2-20000000000000000-2-22200000000000000000000
χ19222222222222-12222-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ20222222222222-12222-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-100000000-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ21222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ22222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ2322222222-2-2-2-2222222222222-2-2-2-2-2-2000000002222222222220000-2-20000000000000000-2-2-2-200000000000000000000
χ2422222222-2-2-2-2222222222222-2-2-2-2-2-2000000002222-2-2-2-2-2-2-2-20000-2-20000000000000000222200000000000000000000
χ2522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-12211112i2i2i2i−2i−2i−2i−2i1111000000002i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-111000000
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χ302222-2-2-2-222-2-2222-2-222-2-22-2-22-222-2-2-2-222-2-222-2-2220000000000002-200000000-2-222-2-222000000000000000000000000
χ312222-2-2-2-222-2-22-2-22222-2-22-2-2-2222-2-20000000022-2-2000000000000-220000000000000000000022-2-222-2-2000000000000
χ322222-2-2-2-222-2-22-2-22222-2-22-2-2-2222-2-20000000022-2-2000000000000-2200000000000000000000-2-222-2-222000000000000
χ332222-2-2-2-222-2-2-122-2-2-1-111-1112-2-1-11122-2-222-2-211-1-1000000000000-1133−3−333−3−3-1-111-1-111000000000000003−33−3000000
χ342222-2-2-2-222-2-2-122-2-2-1-111-1112-2-1-11122-2-222-2-211-1-1000000000000-11−3−333−3−333-1-111-1-11100000000000000−33−33000000
χ352222-2-2-2-222-2-2-122-2-2-1-111-1112-2-1-111-2-222-2-22211-1-1000000000000-1133−3−333−3−311-1-111-1-100000000000000−33−33000000
χ362222-2-2-2-222-2-2-122-2-2-1-111-1112-2-1-111-2-222-2-22211-1-1000000000000-11−3−333−3−33311-1-111-1-1000000000000003−33−3000000
χ372222-2-2-2-2-2-222222-2-222-2-22-2-2-22-2-22200000000-2-222000000000000-22000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
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χ442222-2-2-2-2-2-222-1-2-222-1-111-1112-211-1-1−2i−2i2i2i2i2i−2i−2i-1-111000000000000-11i3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii00000000000000−333−3000000
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χ4622-2-22-22-22-22-2200002-2-2-2-222002-2-222−22−22−22−200000000−2i−2i2i2i000000000000002−22−22−22−200−2i2ii2−i2i2−i2i2−i2i2−i2000000000000
χ4722-2-22-22-22-22-2200002-2-2-2-222002-2-22−22−22−22−22000000002i2i−2i−2i00000000000000−22−22−22−22002i−2ii2−i2i2−i2i2−i2i2−i2000000000000
χ4822-2-22-22-22-22-2200002-2-2-2-222002-2-22−22−22−22−2200000000−2i−2i2i2i00000000000000−22−22−22−2200−2i2i−i2i2−i2i2−i2i2−i2i2000000000000
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χ884-44-4-444-40000-24i−4i−4i4i2-22-222-2000000000000002i−2i−2i2i00000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000000000000000000000000000
χ894-44-4-444-40000-2−4i4i4i−4i2-22-222-200000000000000−2i2i2i−2i00000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000000000000000000000000000
χ904-44-4-444-40000-2−4i4i4i−4i2-22-222-200000000000000−2i2i2i−2i00000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000000000000000000000000000
χ914-4-4444-4-4000040000-4-4-4444-400000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ924-4-4444-4-4000040000-4-4-4444-40000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ934-4-44-4-444000040000-4-44-44-440000000000000000004-4-4400000000000000000000000000000000000000000000000000
χ944-4-44-4-444000040000-4-44-44-44000000000000000000-444-400000000000000000000000000000000000000000000000000
χ958-8-8888-8-80000-40000444-4-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88-8-8880000-4000044-44-44-4000000000000000000000000000000000000000000000000000000000000000000000000

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