Finite Group Databasebeta

← Group #13164622

Character table — Group #13164622

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11222226666661212121212121212121212121818242424242424242424245454727272721122222666666121212121212121212121212181824242424242424242424545472727272
order1223666344666336612121212121212122433666666662466121222266666446666666121212121212121224666666666624661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-11111111111-1-1-1-1-1-11111111111111111111111111-1-11111111111-1-1-1-1-1-1
χ31111111111111−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i321111111111111−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ41111111111111−1+i32−1−i32−1+i32−1−i3211111111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321+i321111111111111−1+i32−1−i32−1+i32−1−i3211111111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321+i32
χ51111111111111−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i321111111111111−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ61111111111111−1−i32−1+i32−1−i32−1+i3211111111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321−i321111111111111−1−i32−1+i32−1−i32−1+i3211111111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321−i32
χ711-11-1-1111-1-1-1111111-1111-1-1-11-111-1-11-1-11-1-1-1111-1-111-11-1-1111-1-1-1111111-1111-1-1-11-111-1-11-1-11-1-1-1111-1-1
χ811-11-1-1111-1-1-1111111-1111-1-1-1-1111-1-11-1-11-1-11-1-1-11111-11-1-1111-1-1-1111111-1111-1-1-1-1111-1-11-1-11-1-11-1-1-111
χ911-11-1-1111-1-1-11−1+i32−1−i32−1+i32−1−i321-1111-1-1-11-1−1+i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i32-11−1+i32−1−i321−i321+i3211-11-1-1111-1-1-11−1+i32−1−i32−1+i32−1−i321-1111-1-1-11-1−1+i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i32-11−1+i32−1−i321−i321+i32
χ1011-11-1-1111-1-1-11−1+i32−1−i32−1+i32−1−i321-1111-1-1-1-11−1+i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i321-11−i321+i32−1+i32−1−i3211-11-1-1111-1-1-11−1+i32−1−i32−1+i32−1−i321-1111-1-1-1-11−1+i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i321-11−i321+i32−1+i32−1−i32
χ1111-11-1-1111-1-1-11−1−i32−1+i32−1−i32−1+i321-1111-1-1-11-1−1−i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i32-11−1−i32−1+i321+i321−i3211-11-1-1111-1-1-11−1−i32−1+i32−1−i32−1+i321-1111-1-1-11-1−1−i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i32-11−1−i32−1+i321+i321−i32
χ1211-11-1-1111-1-1-11−1−i32−1+i32−1−i32−1+i321-1111-1-1-1-11−1−i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i321-11+i321−i32−1−i32−1+i3211-11-1-1111-1-1-11−1−i32−1+i32−1−i32−1+i321-1111-1-1-1-11−1−i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i321-11+i321−i32−1−i32−1+i32
χ132222222-122-1-1-1222222-1-1-1-1-1-100-1-122-1-1-1-1-1-10000002222222-122-1-1-1222222-1-1-1-1-1-100-1-122-1-1-1-1-1-1000000
χ142222222-122-1-1-1−1+i3−1−i3−1+i3−1−i322-1-1-1-1-1-1001−i321+i32−1+i3−1−i31−i321−i321−i321+i321+i321+i320000002222222-122-1-1-1−1+i3−1−i3−1+i3−1−i322-1-1-1-1-1-1001−i321+i32−1+i3−1−i31−i321−i321−i321+i321+i321+i32000000
χ152222222-122-1-1-1−1−i3−1+i3−1−i3−1+i322-1-1-1-1-1-1001+i321−i32−1−i3−1+i31+i321+i321+i321−i321−i321−i320000002222222-122-1-1-1−1−i3−1+i3−1−i3−1+i322-1-1-1-1-1-1001+i321−i32−1−i3−1+i31+i321+i321+i321−i321−i321−i32000000
χ1622-22-2-22-12-211-122222-2-1-1-111100-1-1-2-2-111-11100000022-22-2-22-12-211-122222-2-1-1-111100-1-1-2-2-111-111000000
χ1722-22-2-22-12-211-1−1+i3−1−i3−1+i3−1−i32-2-1-1-1111001−i321+i321−i31+i31−i32−1+i32−1+i321+i32−1−i32−1−i3200000022-22-2-22-12-211-1−1+i3−1−i3−1+i3−1−i32-2-1-1-1111001−i321+i321−i31+i31−i32−1+i32−1+i321+i32−1−i32−1−i32000000
χ1822-22-2-22-12-211-1−1−i3−1+i3−1−i3−1+i32-2-1-1-1111001+i321−i321+i31−i31+i32−1−i32−1−i321−i32−1+i32−1+i3200000022-22-2-22-12-211-1−1−i3−1+i3−1−i3−1+i32-2-1-1-1111001+i321−i321+i31−i31+i32−1−i32−1−i321−i32−1+i32−1+i32000000
χ1933333333-1-13330000-1-1-1-1-1-1-1-1330000000000-1-1000033333333-1-13330000-1-1-1-1-1-1-1-1330000000000-1-10000
χ2033333333-1-13330000-1-1-1-1-1-1-1-1-3-3000000000011000033333333-1-13330000-1-1-1-1-1-1-1-1-3-30000000000110000
χ2133-33-3-333-11-3-330000-11-1-1-11113-300000000001-1000033-33-3-333-11-3-330000-11-1-1-11113-300000000001-10000
χ2233-33-3-333-11-3-330000-11-1-1-1111-330000000000-11000033-33-3-333-11-3-330000-11-1-1-1111-330000000000-110000
χ234-40400-440000-4-2-2220000000000-2-2002002000000004-40400-440000-4-2-2220000000000-2-200200200000000
χ244-40400-440000-41−i31+i3−1+i3−1−i300000000001−i31+i300−1+i300−1−i3000000004-40400-440000-41−i31+i3−1+i3−1−i300000000001−i31+i300−1+i300−1−i300000000
χ254-40400-440000-41+i31−i3−1−i3−1+i300000000001+i31−i300−1−i300−1+i3000000004-40400-440000-41+i31−i3−1−i3−1+i300000000001+i31−i300−1−i300−1+i300000000
χ264-40400-4-2002i3−2i32-2-22200000000001100-1i3−i3-1i3−i30000004-40400-4-2002i3−2i32-2-22200000000001100-1i3−i3-1i3−i3000000
χ274-40400-4-2002i3−2i321−i31+i3−1+i3−1−i30000000000−1+i32−1−i32001−i32−3−i323+i321+i323−i32−3+i320000004-40400-4-2002i3−2i321−i31+i3−1+i3−1−i30000000000−1+i32−1−i32001−i32−3−i323+i321+i323−i32−3+i32000000
χ284-40400-4-2002i3−2i321+i31−i3−1−i3−1+i30000000000−1−i32−1+i32001+i323−i32−3+i321−i32−3−i323+i320000004-40400-4-2002i3−2i321+i31−i3−1−i3−1+i30000000000−1−i32−1+i32001+i323−i32−3+i321−i32−3−i323+i32000000
χ294-40400-4-200−2i32i32-2-22200000000001100-1−i3i3-1−i3i30000004-40400-4-200−2i32i32-2-22200000000001100-1−i3i3-1−i3i3000000
χ304-40400-4-200−2i32i321−i31+i3−1+i3−1−i30000000000−1+i32−1−i32001−i323+i32−3−i321+i32−3+i323−i320000004-40400-4-200−2i32i321−i31+i3−1+i3−1−i30000000000−1+i32−1−i32001−i323+i32−3−i321+i32−3+i323−i32000000
χ314-40400-4-200−2i32i321+i31−i3−1−i3−1+i30000000000−1−i32−1+i32001+i32−3+i323−i321−i323+i32−3−i320000004-40400-4-200−2i32i321+i31−i3−1−i3−1+i30000000000−1−i32−1+i32001+i32−3+i323−i321−i323+i32−3−i32000000
χ326666666-3-2-2-3-3-30000-2-21111110000000000000000006666666-3-2-2-3-3-30000-2-2111111000000000000000000
χ33666-3-3-3-30660000000-3-3000000000000000000000000666-3-3-3-30660000000-3-3000000000000000000000000
χ34666-3-3-3-30-2-20000000114-2-24-2-2000000000000000000666-3-3-3-30-2-20000000114-2-24-2-2000000000000000000
χ35666-3-3-3-30-2-2000000011-24-2-24-2000000000000000000666-3-3-3-30-2-2000000011-24-2-24-2000000000000000000
χ36666-3-3-3-30-2-2000000011-2-24-2-24000000000000000000666-3-3-3-30-2-2000000011-2-24-2-24000000000000000000
χ3766-66-6-66-3-2233-30000-22111-1-1-100000000000000000066-66-6-66-3-2233-30000-22111-1-1-1000000000000000000
χ3866-6-333-306-60000000-3300000000000000000000000066-6-333-306-60000000-33000000000000000000000000
χ3966-6-333-30-2200000001-14-2-2-42200000000000000000066-6-333-30-2200000001-14-2-2-422000000000000000000
χ4066-6-333-30-2200000001-1-24-22-4200000000000000000066-6-333-30-2200000001-1-24-22-42000000000000000000
χ4166-6-333-30-2200000001-1-2-2422-400000000000000000066-6-333-30-2200000001-1-2-2422-4000000000000000000
χ4212-120-66i3−6i3600000000000000000000000000000000000012-120-66i3−6i36000000000000000000000000000000000000
χ4312-120-6−6i36i3600000000000000000000000000000000000012-120-6−6i36i36000000000000000000000000000000000000
χ441111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ451111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ461111111111111−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321−i321+i321+i321+i32-1-11−i321+i321−i321+i32
χ471111111111111−1+i32−1−i32−1+i32−1−i3211111111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321+i32-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-1-1-1-1-1-1-1-1111−i321+i321−i321+i321−i321−i321−i321+i321+i321+i3211−1+i32−1−i32−1+i32−1−i32
χ481111111111111−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321+i321−i321−i321−i32-1-11+i321−i321+i321−i32
χ491111111111111−1−i32−1+i32−1−i32−1+i3211111111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321−i32-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-1-1-1-1-1-1-1-1111+i321−i321+i321−i321+i321+i321+i321−i321−i321−i3211−1−i32−1+i32−1−i32−1+i32
χ5011-11-1-1111-1-1-1111111-1111-1-1-11-111-1-11-1-11-1-1-1111-1-1-1-11-111-1-1-1111-1-1-1-1-1-11-1-1-1111-11-1-111-111-1111-1-1-111
χ5111-11-1-1111-1-1-1111111-1111-1-1-1-1111-1-11-1-11-1-11-1-1-111-1-11-111-1-1-1111-1-1-1-1-1-11-1-1-11111-1-1-111-111-111-1111-1-1
χ5211-11-1-1111-1-1-11−1+i32−1−i32−1+i32−1−i321-1111-1-1-11-1−1+i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i32-11−1+i32−1−i321−i321+i32-1-11-111-1-1-1111-11−i321+i321−i321+i32-11-1-1-1111-111−i321+i32−1+i32−1−i321−i32−1+i32−1+i321+i32−1−i32−1−i321-11−i321+i32−1+i32−1−i32
χ5311-11-1-1111-1-1-11−1+i32−1−i32−1+i32−1−i321-1111-1-1-1-11−1+i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i321-11−i321+i32−1+i32−1−i32-1-11-111-1-1-1111-11−i321+i321−i321+i32-11-1-1-11111-11−i321+i32−1+i32−1−i321−i32−1+i32−1+i321+i32−1−i32−1−i32-11−1+i32−1−i321−i321+i32
χ5411-11-1-1111-1-1-11−1−i32−1+i32−1−i32−1+i321-1111-1-1-11-1−1−i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i32-11−1−i32−1+i321+i321−i32-1-11-111-1-1-1111-11+i321−i321+i321−i32-11-1-1-1111-111+i321−i32−1−i32−1+i321+i32−1−i32−1−i321−i32−1+i32−1+i321-11+i321−i32−1−i32−1+i32
χ5511-11-1-1111-1-1-11−1−i32−1+i32−1−i32−1+i321-1111-1-1-1-11−1−i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i321-11+i321−i32−1−i32−1+i32-1-11-111-1-1-1111-11+i321−i321+i321−i32-11-1-1-11111-11+i321−i32−1−i32−1+i321+i32−1−i32−1−i321−i32−1+i32−1+i32-11−1−i32−1+i321+i321−i32
χ562222222-122-1-1-1222222-1-1-1-1-1-100-1-122-1-1-1-1-1-1000000-2-2-2-2-2-2-21-2-2111-2-2-2-2-2-21111110011-2-2111111000000
χ572222222-122-1-1-1−1+i3−1−i3−1+i3−1−i322-1-1-1-1-1-1001−i321+i32−1+i3−1−i31−i321−i321−i321+i321+i321+i32000000-2-2-2-2-2-2-21-2-21111−i31+i31−i31+i3-2-211111100−1+i32−1−i321−i31+i3−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000
χ582222222-122-1-1-1−1−i3−1+i3−1−i3−1+i322-1-1-1-1-1-1001+i321−i32−1−i3−1+i31+i321+i321+i321−i321−i321−i32000000-2-2-2-2-2-2-21-2-21111+i31−i31+i31−i3-2-211111100−1−i32−1+i321+i31−i3−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000000
χ5922-22-2-22-12-211-122222-2-1-1-111100-1-1-2-2-111-111000000-2-22-222-21-22-1-11-2-2-2-2-22111-1-1-10011221-1-11-1-1000000
χ6022-22-2-22-12-211-1−1+i3−1−i3−1+i3−1−i32-2-1-1-1111001−i321+i321−i31+i31−i32−1+i32−1+i321+i32−1−i32−1−i32000000-2-22-222-21-22-1-111−i31+i31−i31+i3-22111-1-1-100−1+i32−1−i32−1+i3−1−i3−1+i321−i321−i32−1−i321+i321+i32000000
χ6122-22-2-22-12-211-1−1−i3−1+i3−1−i3−1+i32-2-1-1-1111001+i321−i321+i31−i31+i32−1−i32−1−i321−i32−1+i32−1+i32000000-2-22-222-21-22-1-111+i31−i31+i31−i3-22111-1-1-100−1−i32−1+i32−1−i3−1+i3−1−i321+i321+i32−1+i321−i321−i32000000
χ6233333333-1-13330000-1-1-1-1-1-1-1-1330000000000-1-10000-3-3-3-3-3-3-3-311-3-3-3000011111111-3-30000000000110000
χ6333333333-1-13330000-1-1-1-1-1-1-1-1-3-30000000000110000-3-3-3-3-3-3-3-311-3-3-3000011111111330000000000-1-10000
χ6433-33-3-333-11-3-330000-11-1-1-11113-300000000001-10000-3-33-333-3-31-133-300001-1111-1-1-1-330000000000-110000
χ6533-33-3-333-11-3-330000-11-1-1-1111-330000000000-110000-3-33-333-3-31-133-300001-1111-1-1-13-300000000001-10000
χ664-40400-440000-4-2-2220000000000-2-200200200000000-440-4004-40000422-2-200000000002200-200-200000000
χ674-40400-440000-41−i31+i3−1+i3−1−i300000000001−i31+i300−1+i300−1−i300000000-440-4004-400004−1+i3−1−i31−i31+i30000000000−1+i3−1−i3001−i3001+i300000000
χ684-40400-440000-41+i31−i3−1−i3−1+i300000000001+i31−i300−1−i300−1+i300000000-440-4004-400004−1−i3−1+i31+i31−i30000000000−1−i3−1+i3001+i3001−i300000000
χ694-40400-4-2002i3−2i32-2-22200000000001100-1i3−i3-1i3−i3000000-440-4004200−2i32i3-222-2-20000000000-1-1001−i3i31−i3i3000000
χ704-40400-4-2002i3−2i321−i31+i3−1+i3−1−i30000000000−1+i32−1−i32001−i32−3−i323+i321+i323−i32−3+i32000000-440-4004200−2i32i3-2−1+i3−1−i31−i31+i300000000001−i321+i3200−1+i323+i32−3−i32−1−i32−3+i323−i32000000
χ714-40400-4-2002i3−2i321+i31−i3−1−i3−1+i30000000000−1−i32−1+i32001+i323−i32−3+i321−i32−3−i323+i32000000-440-4004200−2i32i3-2−1−i3−1+i31+i31−i300000000001+i321−i3200−1−i32−3+i323−i32−1+i323+i32−3−i32000000
χ724-40400-4-200−2i32i32-2-22200000000001100-1−i3i3-1−i3i3000000-440-40042002i3−2i3-222-2-20000000000-1-1001i3−i31i3−i3000000
χ734-40400-4-200−2i32i321−i31+i3−1+i3−1−i30000000000−1+i32−1−i32001−i323+i32−3−i321+i32−3+i323−i32000000-440-40042002i3−2i3-2−1+i3−1−i31−i31+i300000000001−i321+i3200−1+i32−3−i323+i32−1−i323−i32−3+i32000000
χ744-40400-4-200−2i32i321+i31−i3−1−i3−1+i30000000000−1−i32−1+i32001+i32−3+i323−i321−i323+i32−3−i32000000-440-40042002i3−2i3-2−1−i3−1+i31+i31−i300000000001+i321−i3200−1−i323−i32−3+i32−1+i32−3−i323+i32000000
χ756666666-3-2-2-3-3-30000-2-2111111000000000000000000-6-6-6-6-6-6-6322333000022-1-1-1-1-1-1000000000000000000
χ76666-3-3-3-30660000000-3-3000000000000000000000000-6-6-633330-6-6000000033000000000000000000000000
χ77666-3-3-3-30-2-20000000114-2-24-2-2000000000000000000-6-6-633330220000000-1-1-422-422000000000000000000
χ78666-3-3-3-30-2-2000000011-24-2-24-2000000000000000000-6-6-633330220000000-1-12-422-42000000000000000000
χ79666-3-3-3-30-2-2000000011-2-24-2-24000000000000000000-6-6-633330220000000-1-122-422-4000000000000000000
χ8066-66-6-66-3-2233-30000-22111-1-1-1000000000000000000-6-66-666-632-2-3-3300002-2-1-1-1111000000000000000000
χ8166-6-333-306-60000000-33000000000000000000000000-6-663-3-330-6600000003-3000000000000000000000000
χ8266-6-333-30-2200000001-14-2-2-422000000000000000000-6-663-3-3302-20000000-11-4224-2-2000000000000000000
χ8366-6-333-30-2200000001-1-24-22-42000000000000000000-6-663-3-3302-20000000-112-42-24-2000000000000000000
χ8466-6-333-30-2200000001-1-2-2422-4000000000000000000-6-663-3-3302-20000000-1122-4-2-24000000000000000000
χ8512-120-66i3−6i36000000000000000000000000000000000000-121206−6i36i3-6000000000000000000000000000000000000
χ8612-120-6−6i36i36000000000000000000000000000000000000-1212066i3−6i3-6000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).