Finite Group Databasebeta

← Group #13167022

Character table — Group #13167022

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222224444444444444444448888888888888888991212121212121212121212121818181818181824242424242424242424242436363636363672727272108108108108
order12234461212333366666661212121212121236666661212121212121212122288882424242424242424244661212242424242424242424242424222261266664444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111-1-11-1-111111111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-111-1-111iiiiii−i−i−i−i−i−i11-1-1-1111-1-1ii−i−i
χ61111-1-11-1-111111111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-111-1-111iiiiii−i−i−i−i−i−i-1-111-11-1-111−i−iii
χ71111-1-11-1-111111111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-111-1-111−i−i−i−i−i−iiiiiii11-1-1-1111-1-1−i−iii
χ81111-1-11-1-111111111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-111-1-111−i−i−i−i−i−iiiiiii-1-111-11-1-111ii−i−i
χ911-111-11-1-11111-1-1-111111-1-1-1-1-1-11-1-1-1-1-111111-111-1-1-1-1i−ii−iii−i−iii−i−i11-1-1-111iii−i−i−iiii−i−i−i1-11-11-11-11-1i−ii−i
χ1011-111-11-1-11111-1-1-111111-1-1-1-1-1-11-1-1-1-1-111111-111-1-1-1-1i−ii−iii−i−iii−i−i11-1-1-111iii−i−i−iiii−i−i−i-11-111-1-11-11−ii−ii
χ1111-111-11-1-11111-1-1-111111-1-1-1-1-1-11-1-1-1-1-111111-111-1-1-1-1−ii−ii−i−iii−i−iii11-1-1-111−i−i−iiii−i−i−iiii1-11-11-11-11-1−ii−ii
χ1211-111-11-1-11111-1-1-111111-1-1-1-1-1-11-1-1-1-1-111111-111-1-1-1-1−ii−ii−i−iii−i−iii11-1-1-111−i−i−iiii−i−i−iiii-11-111-1-11-11i−ii−i
χ1311-11-111111111-1-1-11111-11111111-1-1-1-1-11-1-1-1-11-1-111111-1-1111-1-1-1-111-11-11111111-1-1-1-1-1-11111-1-11-1-11-1-111-1-11
χ1411-11-111111111-1-1-11111-11111111-1-1-1-1-11-1-1-1-11-1-111111-1-1111-1-1-1-111-11-11111111-1-1-1-1-1-1111-111-1-1-1-111-1-111-1
χ1511-11-111111111-1-1-11111-11111111-1-1-1-1-11-1-1-1-11-1-11111-111-1-1-11111-1-1-11-11111-1-1-1111111-1-1-11-1-11-1-11-1-11-111-1
χ1611-11-111111111-1-1-11111-11111111-1-1-1-1-11-1-1-1-11-1-11111-111-1-1-11111-1-1-11-11111-1-1-1111111-1-1-1-111-1-1-1-111-11-1-11
χ172222222222222222222222222222222222222222222-2-2000000000000-2-2-2-2-2-2-20000000000000000-2-200000000
χ182222-2-22-2-222222222222-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2220000000000002-2-222-2-200000000000000002-200000000
χ19222-122-1-1-12-1-12-1222-1-12-122-1-1-1-1-12-1-1-1-1-122-1-12-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-12-1-12-1-12-1-12-1-10000-1-100000000
χ20222-122-1-1-12-1-12-1222-1-12-122-1-1-1-1-12-1-1-1-1-122-1-12-1-1-1-122-2-2-2-211111111222-1-1-1-1-211-211-211-2110000-1-100000000
χ21222-122-1-1-12-1-12-1222-1-12-122-1-1-1-1-12-1-1-1-1-122-1-12-1-1-1-1-2-20000−i3i3−i3i3−i3i3−i3i3-2-2-211110−i3i30−i3i30−i3i30−i3i300001100000000
χ22222-122-1-1-12-1-12-1222-1-12-122-1-1-1-1-12-1-1-1-1-122-1-12-1-1-1-1-2-20000i3−i3i3−i3i3−i3i3−i3-2-2-211110i3−i30i3−i30i3−i30i3−i300001100000000
χ23222-1-2-2-1112-1-12-1222-1-121-2-21111-12-1-1-1-1-1-2-211-211112200003−33−3−33−332-2-2-1-11103−303−30−330−330000-1100000000
χ24222-1-2-2-1112-1-12-1222-1-121-2-21111-12-1-1-1-1-1-2-211-21111220000−33−333−33−32-2-2-1-1110−330−3303−303−30000-1100000000
χ25222-1-2-2-1112-1-12-1222-1-121-2-21111-12-1-1-1-1-1-2-211-21111-2-22i2i−2i−2i−i−i−i−iiiii-22211-1-12i−i−i2i−i−i−2iii−2iii00001-100000000
χ26222-1-2-2-1112-1-12-1222-1-121-2-21111-12-1-1-1-1-1-2-211-21111-2-2−2i−2i2i2iiiii−i−i−i−i-22211-1-1−2iii−2iii2i−i−i2i−i−i00001-100000000
χ2722-222-22-2-22222-2-2-222222-2-2-2-2-2-22-2-2-2-2-222222-222-2-222000000000000-2-2222-2-20000000000000000-2200000000
χ2822-22-222222222-2-2-22222-22222222-2-2-2-2-22-2-2-2-22-2-222-2-20000000000002-22-2-2-2-200000000000000002200000000
χ2922-2-12-2-1112-1-121-2-22-1-12-1-2-21111-1-21111-122-1-1-2-1-1112200003−3−333−3−33-2-22-1-11103−30−3303−30−3300001-100000000
χ3022-2-12-2-1112-1-121-2-22-1-12-1-2-21111-1-21111-122-1-1-2-1-111220000−333−3−333−3-2-22-1-1110−3303−30−3303−300001-100000000
χ3122-2-12-2-1112-1-121-2-22-1-12-1-2-21111-1-21111-122-1-1-2-1-111-2-22i−2i2i−2i−i−iii−i−iii22-211-1-12i−i−i−2iii2i−i−i−2iii0000-1100000000
χ3222-2-12-2-1112-1-121-2-22-1-12-1-2-21111-1-21111-122-1-1-2-1-111-2-2−2i2i−2i2iii−i−iii−i−i22-211-1-1−2iii2i−i−i−2iii2i−i−i0000-1100000000
χ3322-2-1-22-1-1-12-1-121-2-22-1-12122-1-1-1-1-1-21111-1-2-211211-1-1222-2-22-1-11111-1-1-22-2-1-1-1-12-1-1-211-2112-1-100001100000000
χ3422-2-1-22-1-1-12-1-121-2-22-1-12122-1-1-1-1-1-21111-1-2-211211-1-122-222-211-1-1-1-111-22-2-1-1-1-1-2112-1-12-1-1-21100001100000000
χ3522-2-1-22-1-1-12-1-121-2-22-1-12122-1-1-1-1-1-21111-1-2-211211-1-1-2-20000−i3i3i3−i3i3−i3−i3i32-2211110−i3i30i3−i30i3−i30−i3i30000-1-100000000
χ3622-2-1-22-1-1-12-1-121-2-22-1-12122-1-1-1-1-1-21111-1-2-211211-1-1-2-20000i3−i3−i3i3−i3i3i3−i32-2211110i3−i30−i3i30−i3i30i3−i30000-1-100000000
χ37444444444111-24-2-2111-24111111-2111-2-2-21-211-2-2-2-2-2002222222222220000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ38444444444111-24-2-2111-24111111-2111-2-2-21-211-2-2-2-2-200-2-2-2-2-2-2-2-2-2-2-2-2000000011111111111100000000000000
χ39444444444-2-2-21411-2-2-214-2-2-2-2-2-21-2-2-2111-21-2-211111000000000000000000000000000000000222200-1-1-1-10000
χ40444444444-2-2-21411-2-2-214-2-2-2-2-2-21-2-2-2111-21-2-211111000000000000000000000000000000000-2-2-2-20011110000
χ414444-4-44-4-4111-24-2-2111-2-4-1-1-1-1-1-1-2111-2-2-2-12-1-122222002i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000−i−i−i−i−i−iiiiiii00000000000000
χ424444-4-44-4-4111-24-2-2111-2-4-1-1-1-1-1-1-2111-2-2-2-12-1-12222200−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000iiiiii−i−i−i−i−i−i00000000000000
χ434444-4-44-4-4-2-2-21411-2-2-21-42222221-2-2-21112-122-1-1-1-1-100000000000000000000000000000000022-2-200-1-1110000
χ444444-4-44-4-4-2-2-21411-2-2-21-42222221-2-2-21112-122-1-1-1-1-1000000000000000000000000000000000-2-2220011-1-10000
χ45444-244-2-2-21−1−3i32−1+3i32-2-2-2-21−1−3i32−1+3i32-2-211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1+3i321111-2−1−3i32−1+3i32-21111002222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i30000000-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i3200000000000000
χ46444-244-2-2-21−1−3i32−1+3i32-2-2-2-21−1−3i32−1+3i32-2-211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1+3i321111-2−1−3i32−1+3i32-2111100-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i300000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ47444-244-2-2-21−1+3i32−1−3i32-2-2-2-21−1+3i32−1−3i32-2-211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1−3i321111-2−1+3i32−1−3i32-21111002222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i30000000-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i3200000000000000
χ48444-244-2-2-21−1+3i32−1−3i32-2-2-2-21−1+3i32−1−3i32-2-211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1−3i321111-2−1+3i32−1−3i32-2111100-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i300000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ49444-2-4-4-2221−1−3i32−1+3i32-2-2-2-21−1−3i32−1+3i32-22-1-11+3i321+3i321−3i321−3i3211−1−3i32−1+3i32111-121+3i321−3i322-1-1-1-1002i2i−2i−2i2ζ112ζ72ζ112ζ7−2ζ11−2ζ7−2ζ11−2ζ70000000−i−ζ11−ζ7−i−ζ11−ζ7iζ11ζ7iζ11ζ700000000000000
χ50444-2-4-4-2221−1−3i32−1+3i32-2-2-2-21−1−3i32−1+3i32-22-1-11+3i321+3i321−3i321−3i3211−1−3i32−1+3i32111-121+3i321−3i322-1-1-1-100−2i−2i2i2i−2ζ11−2ζ7−2ζ11−2ζ72ζ112ζ72ζ112ζ70000000iζ11ζ7iζ11ζ7−i−ζ11−ζ7−i−ζ11−ζ700000000000000
χ51444-2-4-4-2221−1+3i32−1−3i32-2-2-2-21−1+3i32−1−3i32-22-1-11−3i321−3i321+3i321+3i3211−1+3i32−1−3i32111-121−3i321+3i322-1-1-1-1002i2i−2i−2i2ζ72ζ112ζ72ζ11−2ζ7−2ζ11−2ζ7−2ζ110000000−i−ζ7−ζ11−i−ζ7−ζ11iζ7ζ11iζ7ζ1100000000000000
χ52444-2-4-4-2221−1+3i32−1−3i32-2-2-2-21−1+3i32−1−3i32-22-1-11−3i321−3i321+3i321+3i3211−1+3i32−1−3i32111-121−3i321+3i322-1-1-1-100−2i−2i2i2i−2ζ7−2ζ11−2ζ7−2ζ112ζ72ζ112ζ72ζ110000000iζ7ζ11iζ7ζ11−i−ζ7−ζ11−i−ζ7−ζ1100000000000000
χ5344-444-44-4-4111-2-422111-24-1-1-1-1-1-1-2-1-1-122-21-2112-2-222002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i0000000−i−i−iiii−i−i−iiii00000000000000
χ5444-444-44-4-4111-2-422111-24-1-1-1-1-1-1-2-1-1-122-21-2112-2-22200−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i0000000iii−i−i−iiii−i−i−i00000000000000
χ5544-444-44-4-4-2-2-21-4-1-1-2-2-2142222221222-1-11-21-2-2-111-1-10000000000000000000000000000000002-22-200-11-110000
χ5644-444-44-4-4-2-2-21-4-1-1-2-2-2142222221222-1-11-21-2-2-111-1-1000000000000000000000000000000000-22-22001-11-10000
χ5744-44-44444111-2-422111-2-4111111-2-1-1-122-2-12-1-1-222-2-2002-2-2222-2-2-2-2220000000-1-1-1111111-1-1-100000000000000
χ5844-44-44444111-2-422111-2-4111111-2-1-1-122-2-12-1-1-222-2-200-222-2-2-22222-2-20000000111-1-1-1-1-1-111100000000000000
χ5944-44-44444-2-2-21-4-1-1-2-2-21-4-2-2-2-2-2-21222-1-112-1221-1-1110000000000000000000000000000000002-2-2200-111-10000
χ6044-44-44444-2-2-21-4-1-1-2-2-21-4-2-2-2-2-2-21222-1-112-1221-1-111000000000000000000000000000000000-222-2001-1-110000
χ6144-4-24-4-2221−1−3i32−1+3i32-22221−1−3i32−1+3i32-2-2-1-11+3i321+3i321−3i321−3i321-11+3i321−3i32-1-111-2−1−3i32−1+3i32211-1-1002i−2i2i−2i2ζ112ζ7−2ζ11−2ζ72ζ112ζ7−2ζ11−2ζ70000000−i−ζ11−ζ7iζ11ζ7−i−ζ11−ζ7iζ11ζ700000000000000
χ6244-4-24-4-2221−1−3i32−1+3i32-22221−1−3i32−1+3i32-2-2-1-11+3i321+3i321−3i321−3i321-11+3i321−3i32-1-111-2−1−3i32−1+3i32211-1-100−2i2i−2i2i−2ζ11−2ζ72ζ112ζ7−2ζ11−2ζ72ζ112ζ70000000iζ11ζ7−i−ζ11−ζ7iζ11ζ7−i−ζ11−ζ700000000000000
χ6344-4-24-4-2221−1+3i32−1−3i32-22221−1+3i32−1−3i32-2-2-1-11−3i321−3i321+3i321+3i321-11−3i321+3i32-1-111-2−1+3i32−1−3i32211-1-1002i−2i2i−2i2ζ72ζ11−2ζ7−2ζ112ζ72ζ11−2ζ7−2ζ110000000−i−ζ7−ζ11iζ7ζ11−i−ζ7−ζ11iζ7ζ1100000000000000
χ6444-4-24-4-2221−1+3i32−1−3i32-22221−1+3i32−1−3i32-2-2-1-11−3i321−3i321+3i321+3i321-11−3i321+3i32-1-111-2−1+3i32−1−3i32211-1-100−2i2i−2i2i−2ζ7−2ζ112ζ72ζ11−2ζ7−2ζ112ζ72ζ110000000iζ7ζ11−i−ζ7−ζ11iζ7ζ11−i−ζ7−ζ1100000000000000
χ6544-4-2-44-2-2-21−1−3i32−1+3i32-22221−1−3i32−1+3i32-2211−1−3i32−1−3i32−1+3i32−1+3i321-11+3i321−3i32-1-11-121+3i321−3i32-2-1-111002-2-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i30000000-11+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i3200000000000000
χ6644-4-2-44-2-2-21−1−3i32−1+3i32-22221−1−3i32−1+3i32-2211−1−3i32−1−3i32−1+3i32−1+3i321-11+3i321−3i32-1-11-121+3i321−3i32-2-1-11100-222-21+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i300000001−1−i32−1+i32-11+i321−i32-11+i321−i321−1−i32−1+i3200000000000000
χ6744-4-2-44-2-2-21−1+3i32−1−3i32-22221−1+3i32−1−3i32-2211−1+3i32−1+3i32−1−3i32−1−3i321-11−3i321+3i32-1-11-121−3i321+3i32-2-1-111002-2-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i30000000-11−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i3200000000000000
χ6844-4-2-44-2-2-21−1+3i32−1−3i32-22221−1+3i32−1−3i32-2211−1+3i32−1+3i32−1−3i32−1−3i321-11−3i321+3i32-1-11-121−3i321+3i32-2-1-11100-222-21−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i300000001−1+i32−1−i32-11−i321+i32-11−i321+i321−1+i32−1−i3200000000000000
χ694-40400-4004444000-4-4-4-40000000400000-40000000004-40000000000000004-40000000000000000000000000000
χ704-40400-4004444000-4-4-4-40000000400000-4000000000-44000000000000000-440000000000000000000000000000
χ714-40-200223−234-2-24000-422-400023−2323−23-2000002000000023−234-4000000000000000-2223−2300000000000000000000000000
χ724-40-200223−234-2-24000-422-400023−2323−23-2000002000000023−23-440000000000000002-2−232300000000000000000000000000
χ734-40-2002−23234-2-24000-422-4000−2323−2323-20000020000000−23234-4000000000000000-22−232300000000000000000000000000
χ744-40-2002−23234-2-24000-422-4000−2323−2323-20000020000000−2323-440000000000000002-223−2300000000000000000000000000
χ75888-488-4-4-4-4222-422-4222-4-4-42222-1-422-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000
χ76888-4-8-8-444-4222-422-4222444-2-2-2-2-1-422-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000
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χ798-80800-800222-4000-2-2-2406i−6i6i−6i−6i6i-400000400000000000000000000000000000000000000000000000000000000
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χ818-80800-800-4-4-4206-6444-2000000020006-6-200000000000000000000000000000000000000000000000000000000
χ828-80800-800-4-4-420-66444-200000002000-66-200000000000000000000000000000000000000000000000000000000
χ838-80-400443−432−1−3i3−1+3i3-4000-21+3i31−3i3406i−6i2ζ7+4ζ11−2ζ7−4ζ11−4ζ7−2ζ114ζ7+2ζ11200000-20000000−232300000000000000000000000000000000000000000000000
χ848-80-400443−432−1+3i3−1−3i3-4000-21−3i31+3i340−6i6i−4ζ7−2ζ114ζ7+2ζ112ζ7+4ζ11−2ζ7−4ζ11200000-20000000−232300000000000000000000000000000000000000000000000
χ858-80-400443−43-422206-64-2-2-2000−2323−2323-1000-3310000033−333−300000000000000000000000000000000000000000000000
χ868-80-400443−43-42220-664-2-2-2000−2323−2323-10003-3100000−33333−300000000000000000000000000000000000000000000000
χ878-80-4004−43432−1−3i3−1+3i3-4000-21+3i31−3i340−6i6i−2ζ7−4ζ112ζ7+4ζ114ζ7+2ζ11−4ζ7−2ζ11200000-2000000023−2300000000000000000000000000000000000000000000000
χ888-80-4004−43432−1+3i3−1−3i3-4000-21−3i31+3i3406i−6i4ζ7+2ζ11−4ζ7−2ζ11−2ζ7−4ζ112ζ7+4ζ11200000-2000000023−2300000000000000000000000000000000000000000000000
χ898-80-4004−4343-422206-64-2-2-200023−2323−23-1000-33100000−3333−3300000000000000000000000000000000000000000000000
χ908-80-4004−4343-42220-664-2-2-200023−2323−23-10003-310000033−33−3300000000000000000000000000000000000000000000000

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