Finite Group Databasebeta

← Group #69397

Character table — Group #69397

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222244444444444444444121212122424111122222222222244444444444444444121212122424
order122222344666666644444121212121212121212121212888824222222644666666644444121212121212121212121212888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-1
χ311111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ51111-1-11-1-111-1-11-1-11ii−i−i11-1-1iiii−i−i−i−iii−i−i1-11111-1-11-1-111-1-11-1-11ii−i−i11-1-1iiii−i−i−i−iii−i−i1-1
χ61111-1-11-1-111-1-11-1-11ii−i−i11-1-1iiii−i−i−i−i−i−iii-111111-1-11-1-111-1-11-1-11ii−i−i11-1-1iiii−i−i−i−i−i−iii-11
χ71111-1-11-1-111-1-11-1-11−i−iii11-1-1−i−i−i−iiiiiii−i−i-111111-1-11-1-111-1-11-1-11−i−iii11-1-1−i−i−i−iiiiiii−i−i-11
χ81111-1-11-1-111-1-11-1-11−i−iii11-1-1−i−i−i−iiiii−i−iii1-11111-1-11-1-111-1-11-1-11−i−iii11-1-1−i−i−i−iiiii−i−iii1-1
χ92222222-2-22222222-20000-2-2-2-2000000000000002222222-2-22222222-20000-2-2-2-200000000000000
χ10222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1000000222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1000000
χ11222222-122-1-1-1-1-1-1-12-2-2-2-2-1-1-1-111111111000000222222-122-1-1-1-1-1-1-12-2-2-2-2-1-1-1-111111111000000
χ12222222-1-2-2-1-1-1-1-1-1-1-200001111−i3−i3i3i3−i3−i3i3i3000000222222-1-2-2-1-1-1-1-1-1-1-200001111−i3−i3i3i3−i3−i3i3i3000000
χ13222222-1-2-2-1-1-1-1-1-1-1-200001111i3i3−i3−i3i3i3−i3−i3000000222222-1-2-2-1-1-1-1-1-1-1-200001111i3i3−i3−i3i3i3−i3−i3000000
χ142222-2-222222-2-22-2-2-20000-2-222000000000000002222-2-222222-2-22-2-2-20000-2-22200000000000000
χ152222-2-2-122-1-111-111-2000011-1-133−3−3−3−3330000002222-2-2-122-1-111-111-2000011-1-133−3−3−3−333000000
χ162222-2-2-122-1-111-111-2000011-1-1−3−33333−3−30000002222-2-2-122-1-111-111-2000011-1-1−3−33333−3−3000000
χ172222-2-2-1-2-2-1-111-11122i2i−2i−2i-1-111−i−i−i−iiiii0000002222-2-2-1-2-2-1-111-11122i2i−2i−2i-1-111−i−i−i−iiiii000000
χ182222-2-2-1-2-2-1-111-1112−2i−2i2i2i-1-111iiii−i−i−i−i0000002222-2-2-1-2-2-1-111-1112−2i−2i2i2i-1-111iiii−i−i−i−i000000
χ1922-2-20022i−2i2-200-20001+i−1−i1−i−1+i002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000022-2-20022i−2i2-200-20001+i−1−i1−i−1+i002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000
χ2022-2-20022i−2i2-200-2000−1−i1+i−1+i1−i002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000022-2-20022i−2i2-200-2000−1−i1+i−1+i1−i002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000
χ2122-2-2002−2i2i2-200-20001−i−1+i1+i−1−i00−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000022-2-2002−2i2i2-200-20001−i−1+i1+i−1−i00−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000
χ2222-2-2002−2i2i2-200-2000−1+i1−i−1−i1+i00−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000022-2-2002−2i2i2-200-2000−1+i1−i−1−i1+i00−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000
χ2322-2-200-12i−2i-11−i3i31−i3i301+i−1−i1−i−1+i3−3−ii−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ2200000022-2-200-12i−2i-11−i3i31−i3i301+i−1−i1−i−1+i3−3−ii−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22000000
χ2422-2-200-12i−2i-11−i3i31−i3i30−1−i1+i−1+i1−i3−3−iiζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ2200000022-2-200-12i−2i-11−i3i31−i3i30−1−i1+i−1+i1−i3−3−iiζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22000000
χ2522-2-200-12i−2i-11i3−i31i3−i301+i−1−i1−i−1+i−33−ii−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ1400000022-2-200-12i−2i-11i3−i31i3−i301+i−1−i1−i−1+i−33−ii−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14000000
χ2622-2-200-12i−2i-11i3−i31i3−i30−1−i1+i−1+i1−i−33−iiζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ1400000022-2-200-12i−2i-11i3−i31i3−i30−1−i1+i−1+i1−i−33−iiζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14000000
χ2722-2-200-1−2i2i-11−i3i31−i3i301−i−1+i1+i−1−i−33i−i−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ2200000022-2-200-1−2i2i-11−i3i31−i3i301−i−1+i1+i−1−i−33i−i−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000
χ2822-2-200-1−2i2i-11−i3i31−i3i30−1+i1−i−1−i1+i−33i−iζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ2200000022-2-200-1−2i2i-11−i3i31−i3i30−1+i1−i−1−i1+i−33i−iζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000
χ2922-2-200-1−2i2i-11i3−i31i3−i301−i−1+i1+i−1−i3−3i−i−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ1400000022-2-200-1−2i2i-11i3−i31i3−i301−i−1+i1+i−1−i3−3i−i−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14000000
χ3022-2-200-1−2i2i-11i3−i31i3−i30−1+i1−i−1−i1+i3−3i−iζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ1400000022-2-200-1−2i2i-11i3−i31i3−i30−1+i1−i−1−i1+i3−3i−iζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000
χ312-2-222-2200-2222-2-2-200000000000000000−i2i2−i2i2002-2-222-2200-2222-2-2-200000000000000000−i2i2−i2i200
χ322-2-222-2200-2222-2-2-200000000000000000i2−i2i2−i2002-2-222-2200-2222-2-2-200000000000000000i2−i2i2−i200
χ332-2-22-22200-22-2-2-222000000000000000002−2−22002-2-22-22200-22-2-2-222000000000000000002−2−2200
χ342-2-22-22200-22-2-2-22200000000000000000−222−2002-2-22-22200-22-2-2-22200000000000000000−222−200
χ354-44-400400-4-400400000000000000000000000004-44-400400-4-40040000000000000000000000000
χ364-44-400-20022−2i32i3-22i3−2i3000000000000000000000004-44-400-20022−2i32i3-22i3−2i300000000000000000000000
χ374-44-400-200222i3−2i3-2−2i32i3000000000000000000000004-44-400-200222i3−2i3-2−2i32i300000000000000000000000
χ384-4-444-4-2002-2-2-2222000000000000000000000004-4-444-4-2002-2-2-222200000000000000000000000
χ394-4-44-44-2002-2222-2-2000000000000000000000004-4-44-44-2002-2222-2-200000000000000000000000
χ40111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ4211111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111
χ4311111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1
χ441111-1-11-1-111-1-11-1-11ii−i−i11-1-1iiii−i−i−i−iii−i−i1-1-1-1-1-111-111-1-111-111-1−i−iii-1-111−i−i−i−iiiii−i−iii-11
χ451111-1-11-1-111-1-11-1-11ii−i−i11-1-1iiii−i−i−i−i−i−iii-11-1-1-1-111-111-1-111-111-1−i−iii-1-111−i−i−i−iiiiiii−i−i1-1
χ461111-1-11-1-111-1-11-1-11−i−iii11-1-1−i−i−i−iiiiiii−i−i-11-1-1-1-111-111-1-111-111-1ii−i−i-1-111iiii−i−i−i−i−i−iii1-1
χ471111-1-11-1-111-1-11-1-11−i−iii11-1-1−i−i−i−iiiii−i−iii1-1-1-1-1-111-111-1-111-111-1ii−i−i-1-111iiii−i−i−i−iii−i−i-11
χ482222222-2-22222222-20000-2-2-2-200000000000000-2-2-2-2-2-2-222-2-2-2-2-2-2-220000222200000000000000
χ49222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-2-2-2-2-21-2-21111111-2-2-2-2-2111111111111000000
χ50222222-122-1-1-1-1-1-1-12-2-2-2-2-1-1-1-111111111000000-2-2-2-2-2-21-2-21111111-222221111-1-1-1-1-1-1-1-1000000
χ51222222-1-2-2-1-1-1-1-1-1-1-200001111−i3−i3i3i3−i3−i3i3i3000000-2-2-2-2-2-2122111111120000-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000
χ52222222-1-2-2-1-1-1-1-1-1-1-200001111i3i3−i3−i3i3i3−i3−i3000000-2-2-2-2-2-2122111111120000-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000
χ532222-2-222222-2-22-2-2-20000-2-22200000000000000-2-2-2-222-2-2-2-2-222-2222000022-2-200000000000000
χ542222-2-2-122-1-111-111-2000011-1-133−3−3−3−333000000-2-2-2-2221-2-211-1-11-1-120000-1-111−3−33333−3−3000000
χ552222-2-2-122-1-111-111-2000011-1-1−3−33333−3−3000000-2-2-2-2221-2-211-1-11-1-120000-1-11133−3−3−3−333000000
χ562222-2-2-1-2-2-1-111-11122i2i−2i−2i-1-111−i−i−i−iiiii000000-2-2-2-22212211-1-11-1-1-2−2i−2i2i2i11-1-1iiii−i−i−i−i000000
χ572222-2-2-1-2-2-1-111-1112−2i−2i2i2i-1-111iiii−i−i−i−i000000-2-2-2-22212211-1-11-1-1-22i2i−2i−2i11-1-1−i−i−i−iiiii000000
χ5822-2-20022i−2i2-200-20001+i−1−i1−i−1+i002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000-2-22200-2−2i2i-22002000−1−i1+i−1+i1−i00−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000
χ5922-2-20022i−2i2-200-2000−1−i1+i−1+i1−i002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000-2-22200-2−2i2i-220020001+i−1−i1−i−1+i00−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000
χ6022-2-2002−2i2i2-200-20001−i−1+i1+i−1−i00−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000-2-22200-22i−2i-22002000−1+i1−i−1−i1+i002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000
χ6122-2-2002−2i2i2-200-2000−1+i1−i−1−i1+i00−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000-2-22200-22i−2i-220020001−i−1+i1+i−1−i002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000
χ6222-2-200-12i−2i-11−i3i31−i3i301+i−1−i1−i−1+i3−3−ii−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22000000-2-222001−2i2i1-1i3−i3-1i3−i30−1−i1+i−1+i1−i−33i−iζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22000000
χ6322-2-200-12i−2i-11−i3i31−i3i30−1−i1+i−1+i1−i3−3−iiζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22000000-2-222001−2i2i1-1i3−i3-1i3−i301+i−1−i1−i−1+i−33i−i−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22000000
χ6422-2-200-12i−2i-11i3−i31i3−i301+i−1−i1−i−1+i−33−ii−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14000000-2-222001−2i2i1-1−i3i3-1−i3i30−1−i1+i−1+i1−i3−3i−iζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14000000
χ6522-2-200-12i−2i-11i3−i31i3−i30−1−i1+i−1+i1−i−33−iiζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14000000-2-222001−2i2i1-1−i3i3-1−i3i301+i−1−i1−i−1+i3−3i−i−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14000000
χ6622-2-200-1−2i2i-11−i3i31−i3i301−i−1+i1+i−1−i−33i−i−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000-2-2220012i−2i1-1i3−i3-1i3−i30−1+i1−i−1−i1+i3−3−iiζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000
χ6722-2-200-1−2i2i-11−i3i31−i3i30−1+i1−i−1−i1+i−33i−iζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000-2-2220012i−2i1-1i3−i3-1i3−i301−i−1+i1+i−1−i3−3−ii−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000
χ6822-2-200-1−2i2i-11i3−i31i3−i301−i−1+i1+i−1−i3−3i−i−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14000000-2-2220012i−2i1-1−i3i3-1−i3i30−1+i1−i−1−i1+i−33−iiζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000
χ6922-2-200-1−2i2i-11i3−i31i3−i30−1+i1−i−1−i1+i3−3i−iζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000-2-2220012i−2i1-1−i3i3-1−i3i301−i−1+i1+i−1−i−33−ii−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14000000
χ702-2-222-2200-2222-2-2-200000000000000000−i2i2−i2i200-222-2-22-2002-2-2-222200000000000000000i2−i2i2−i200
χ712-2-222-2200-2222-2-2-200000000000000000i2−i2i2−i200-222-2-22-2002-2-2-222200000000000000000−i2i2−i2i200
χ722-2-22-22200-22-2-2-222000000000000000002−2−2200-222-22-2-2002-2222-2-200000000000000000−222−200
χ732-2-22-22200-22-2-2-22200000000000000000−222−200-222-22-2-2002-2222-2-2000000000000000002−2−2200
χ744-44-400400-4-40040000000000000000000000000-44-4400-4004400-40000000000000000000000000
χ754-44-400-20022−2i32i3-22i3−2i300000000000000000000000-44-4400200-2-22i3−2i32−2i32i300000000000000000000000
χ764-44-400-200222i3−2i3-2−2i32i300000000000000000000000-44-4400200-2-2−2i32i322i3−2i300000000000000000000000
χ774-4-444-4-2002-2-2-222200000000000000000000000-444-4-44200-2222-2-2-200000000000000000000000
χ784-4-44-44-2002-2222-2-200000000000000000000000-444-44-4200-22-2-2-22200000000000000000000000

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