Finite Group Databasebeta

← Group #10696656

Character table — Group #10696656

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order12223444444666244466121212121212121288881212242424242424242444881212121224242424888888882244
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-111-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-1-11
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ9222222222-2-2222-2-2-22-2-2222-2-2-2-220000-220000000000000000000000000000200-2
χ10222222222-2-2222-2-2-22-2-2222-2-2-2-220000-220000000000000000000000000000-2002
χ11222222-2-2222222-22-2-2-2-22-2-222-2-2200002-2000000000000000000000000000002-20
χ12222222-2-2222222-22-2-2-2-22-2-222-2-2200002-200000000000000000000000000000-220
χ13222222-2-22-2-22222-22-2222-2-2-2-22220000-2-200000000002-2000022-2-2000000000000
χ14222222-2-22-2-22222-22-2222-2-2-2-22220000-2-20000000000-220000-2-222000000000000
χ1522222-222-222222-2-22-2-2-2-2222222-20000-2-20000000000000000000022-2-200000000
χ1622222-222-222222-2-22-2-2-2-2222222-20000-2-200000000000000000000-2-22200000000
χ1722222-222-2-2-222222-2-222-222-2-2-2-2-22i2i−2i−2i2-22i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ1822222-222-2-2-222222-2-222-222-2-2-2-2-2−2i−2i2i2i2-2−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ1922222-2-2-2-2222222-2-2222-2-2-222-2-2-20000-22000000002-20022-2-20000000000000000
χ2022222-2-2-2-2222222-2-2222-2-2-222-2-2-20000-2200000000-2200-2-2220000000000000000
χ2122222-2-2-2-2-2-2222-2222-2-2-2-2-2-2-222-200002200000000000000000000000022-2-20000
χ2222222-2-2-2-2-2-2222-2222-2-2-2-2-2-2-222-2000022000000000000000000000000-2-2220000
χ232222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ242222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ252222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ262222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ272222-12-2-22-2-2-1-1-12-22-2-1-1-11111-1-1-1000011−i3−i3i3i3−i3−i3i3i3002-2−i3i3−i3i3-1-111000000000000
χ282222-12-2-22-2-2-1-1-12-22-2-1-1-11111-1-1-1000011−i3−i3i3i3−i3−i3i3i300-22i3−i3i3−i311-1-1000000000000
χ292222-12-2-22-2-2-1-1-12-22-2-1-1-11111-1-1-1000011i3i3−i3−i3i3i3−i3−i3002-2i3−i3i3−i3-1-111000000000000
χ302222-12-2-22-2-2-1-1-12-22-2-1-1-11111-1-1-1000011i3i3−i3−i3i3i3−i3−i300-22−i3i3−i3i311-1-1000000000000
χ312222-1-222-2-2-2-1-1-122-2-2-1-11-1-1111112i2i−2i−2i-11−i−i−i−iiiii0000−i3i3i3−i33−33−3000000000000
χ322222-1-222-2-2-2-1-1-122-2-2-1-11-1-1111112i2i−2i−2i-11−i−i−i−iiiii0000i3−i3−i3i3−33−33000000000000
χ332222-1-222-2-2-2-1-1-122-2-2-1-11-1-111111−2i−2i2i2i-11iiii−i−i−i−i0000−i3i3i3−i3−33−33000000000000
χ342222-1-222-2-2-2-1-1-122-2-2-1-11-1-111111−2i−2i2i2i-11iiii−i−i−i−i0000i3−i3−i3i33−33−3000000000000
χ352222-1-2-2-2-222-1-1-12-2-22-1-1111-1-111100001-133−3−3−3−3332-200-1-1113−3−33000000000000
χ362222-1-2-2-2-222-1-1-12-2-22-1-1111-1-111100001-133−3−3−3−333-220011-1-1−333−3000000000000
χ372222-1-2-2-2-222-1-1-12-2-22-1-1111-1-111100001-1−3−33333−3−32-200-1-111−333−3000000000000
χ382222-1-2-2-2-222-1-1-12-2-22-1-1111-1-111100001-1−3−33333−3−3-220011-1-13−3−33000000000000
χ394444-24444-4-4-2-2-2-4-4-4422-2-2-22222-200002-200000000000000000000000000000000
χ404444-24-4-4444-2-2-2-44-4-422-222-2-222-20000-2200000000000000000000000000000000
χ414444-2-444-444-2-2-2-4-44-4222-2-2-2-2-2-2200002200000000000000000000000000000000
χ424444-2-4-4-4-4-4-4-2-2-2-44442222222-2-220000-2-200000000000000000000000000000000
χ4344-4-44400-4004-4-40000004000000-42-22-2002-22-22-22-2000000000000000000000000
χ4444-4-44400-4004-4-40000004000000-4-22-2200-22-22-22-22000000000000000000000000
χ4544-4-44-4004004-4-4000000-400000042i−2i−2i2i002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ4644-4-44-4004004-4-4000000-40000004−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4744-4-4-2400-400-2220000−2i32i3-20000−2i32i322-22-200−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3000000000000000000000000
χ4844-4-4-2400-400-2220000−2i32i3-20000−2i32i32-22-22001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000000000000000000000000
χ4944-4-4-2400-400-22200002i3−2i3-200002i3−2i322-22-200−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3000000000000000000000000
χ5044-4-4-2400-400-22200002i3−2i3-200002i3−2i32-22-22001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3000000000000000000000000
χ5144-4-4-2-400400-2220000−2i32i3200002i3−2i3-22i−2i−2i2i002ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ14000000000000000000000000
χ5244-4-4-2-400400-2220000−2i32i3200002i3−2i3-2−2i2i2i−2i00−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ14000000000000000000000000
χ5344-4-4-2-400400-22200002i3−2i320000−2i32i3-22i−2i−2i2i002ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ22000000000000000000000000
χ5444-4-4-2-400400-22200002i3−2i320000−2i32i3-2−2i2i2i−2i00−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ22000000000000000000000000
χ554-44-4404-4000-44-400000004-4000000000000000000000000000000000−2i22i200000000
χ564-44-4404-4000-44-400000004-40000000000000000000000000000000002i2−2i200000000
χ574-44-440-44000-44-40000000-440000000000000000000000000000000−2i22i20000000000
χ584-44-440-44000-44-40000000-4400000000000000000000000000000002i2−2i20000000000
χ594-4-44400004-4-4-440000000004-40000000000000000000000000000000002-22-20000
χ604-4-44400004-4-4-440000000004-4000000000000000000000000000000000-22-220000
χ614-4-4440000-44-4-44000000000-440000000000000000000000000000000002-2-220000
χ624-4-4440000-44-4-44000000000-44000000000000000000000000000000000-222-20000
χ638-88-8-408-80004-440000000-440000000000000000000000000000000000000000000
χ648-88-8-40-880004-4400000004-40000000000000000000000000000000000000000000
χ658-8-88-400008-844-4000000000-4400000000000000000000000000000000000000000
χ668-8-88-40000-8844-40000000004-400000000000000000000000000000000000000000

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