Finite Group Databasebeta

← Group #10699169

Character table — Group #10699169

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order122234444666244441212121212121212121268888122424242424242424888824242424242424248888444488
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111
χ51111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111
χ61111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-11-11-1-1
χ81111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-11-111
χ9222222222222-2-2-2-2222-2-222-2-2-2-2-200002000000002-20022-2-200000000000000
χ10222222222222-2-2-2-2222-2-222-2-2-2-2-20000200000000-2200-2-22200000000000000
χ112222222-2-22222-22-2-222-2-2-2-222-2-222i2i−2i−2i-22i2i2i2i−2i−2i−2i−2i0000000000000000000000
χ122222222-2-22222-22-2-222-2-2-2-222-2-22−2i−2i2i2i-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000
χ132222222-2-2222-22-22-22222-2-2-2-222-20000-200000000002i−2i00002i2i−2i−2i0000000000
χ142222222-2-2222-22-22-22222-2-2-2-222-20000-20000000000−2i2i0000−2i−2i2i2i0000000000
χ1522222-2-2222222-2-22-2-2-2-2-222-2-22220000-2000000000000000000000000020-200
χ1622222-2-2222222-2-22-2-2-2-2-222-2-22220000-20000000000000000000000000-20200
χ1722222-2-222222-222-2-2-2-2222222-2-2-20000-200000000000000000000000020-2000
χ1822222-2-222222-222-2-2-2-2222222-2-2-20000-2000000000000000000000000-202000
χ1922222-2-2-2-222222-2-22-2-222-2-2-2-2-2-220000200000000000000000000000000002i−2i
χ2022222-2-2-2-222222-2-22-2-222-2-2-2-2-2-22000020000000000000000000000000000−2i2i
χ2122222-2-2-2-2222-2-2222-2-2-2-2-2-22222-2000020000000000000000000022-2-2000000
χ2222222-2-2-2-2222-2-2222-2-2-2-2-2-22222-20000200000000000000000000-2-222000000
χ232222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ242222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ252222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-11111111122-2-2-1-1-1-111110000000000
χ262222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-111111111-2-2221111-1-1-1-10000000000
χ272222-12222-1-1-1-2-2-2-22-1-111-1-1111110000-133−3−333−3−32-200-1-1113−33−30000000000
χ282222-12222-1-1-1-2-2-2-22-1-111-1-1111110000-133−3−333−3−3-220011-1-1−33−330000000000
χ292222-12222-1-1-1-2-2-2-22-1-111-1-1111110000-1−3−333−3−3332-200-1-111−33−330000000000
χ302222-12222-1-1-1-2-2-2-22-1-111-1-1111110000-1−3−333−3−333-220011-1-13−33−30000000000
χ312222-122-2-2-1-1-12-22-2-2-1-11111-1-111-12i2i−2i−2i1−i−i−i−iiiii00003−33−3−i3i3i3−i30000000000
χ322222-122-2-2-1-1-12-22-2-2-1-11111-1-111-12i2i−2i−2i1−i−i−i−iiiii0000−33−33i3−i3−i3i30000000000
χ332222-122-2-2-1-1-12-22-2-2-1-11111-1-111-1−2i−2i2i2i1iiii−i−i−i−i00003−33−3i3−i3−i3i30000000000
χ342222-122-2-2-1-1-12-22-2-2-1-11111-1-111-1−2i−2i2i2i1iiii−i−i−i−i0000−33−33−i3i3i3−i30000000000
χ352222-122-2-2-1-1-1-22-22-2-1-1-1-11111-1-1100001−i3−i3i3i3i3i3−i3−i3002i−2i−333−3−i−iii0000000000
χ362222-122-2-2-1-1-1-22-22-2-1-1-1-11111-1-1100001−i3−i3i3i3i3i3−i3−i300−2i2i3−3−33ii−i−i0000000000
χ372222-122-2-2-1-1-1-22-22-2-1-1-1-11111-1-1100001i3i3−i3−i3−i3−i3i3i3002i−2i3−3−33−i−iii0000000000
χ382222-122-2-2-1-1-1-22-22-2-1-1-1-11111-1-1100001i3i3−i3−i3−i3−i3i3i300−2i2i−333−3ii−i−i0000000000
χ394444-2-4-444-2-2-24-4-44-42222-2-222-2-2-200002000000000000000000000000000000
χ404444-2-4-444-2-2-2-444-4-422-2-2-2-2-2-222200002000000000000000000000000000000
χ414444-2-4-4-4-4-2-2-244-4-4422-2-2222222-20000-2000000000000000000000000000000
χ424444-2-4-4-4-4-2-2-2-4-4444222222-2-2-2-220000-2000000000000000000000000000000
χ4344-4-44004-44-4-40000000004-4000002-22-202-22-22-22-20000000000000000000000
χ4444-4-44004-44-4-40000000004-400000-22-220-22-22-22-220000000000000000000000
χ4544-4-4400-444-4-4000000000-44000002i−2i−2i2i02i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ4644-4-4400-444-4-4000000000-4400000−2i2i2i−2i0−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ4744-4-4-2004-4-222000000023−23-2223−230002-22-20−1+31−3−1−31+3−1+31−3−1−31+30000000000000000000000
χ4844-4-4-2004-4-222000000023−23-2223−23000-22-2201−3−1+31+3−1−31−3−1+31+3−1−30000000000000000000000
χ4944-4-4-2004-4-2220000000−2323-22−23230002-22-20−1−31+3−1+31−3−1−31+3−1+31−30000000000000000000000
χ5044-4-4-2004-4-2220000000−2323-22−2323000-22-2201+3−1−31−3−1+31+3−1−31−3−1+30000000000000000000000
χ5144-4-4-200-44-222000000023−232-2−23230002i−2i−2i2i0−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ5244-4-4-200-44-222000000023−232-2−2323000−2i2i2i−2i0ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ5344-4-4-200-44-2220000000−23232-223−230002i−2i−2i2i0ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ5444-4-4-200-44-2220000000−23232-223−23000−2i2i2i−2i0−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000
χ554-4-4444i−4i00-44-4000004i−4i00000000000000000000000000000000002-22i−2i000000
χ564-4-4444i−4i00-44-4000004i−4i0000000000000000000000000000000000-22−2i2i000000
χ574-4-444−4i4i00-44-400000−4i4i00000000000000000000000000000000002-2−2i2i000000
χ584-4-444−4i4i00-44-400000−4i4i0000000000000000000000000000000000-222i−2i000000
χ598-88-880000-8-88000000000000000000000000000000000000000000000000000
χ608-88-8-4000044-4000000000000043−43000000000000000000000000000000000000
χ618-88-8-4000044-40000000000000−4343000000000000000000000000000000000000
χ628-8-88-48i−8i004-4400000−4i4i00000000000000000000000000000000000000000000
χ638-8-88-4−8i8i004-44000004i−4i00000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.