Finite Group Databasebeta

← Group #72242413

Character table — Group #72242413

Order 3456.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11224444666888888121212121212161618181824242424242424323232323636363636484848484848484848484854646464647272727296969696969696108108144144144144144
order1236336624433366628121224243624466666121233664468866121212242424242424233661212122466666612281212122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111-1-111-1-111111-11111111111-1-11-1-1-1-1111-1-1-1-1-1-111111-111-1-1-111111-1-1-1-11-1-1
χ311111111-111111111111111111-1-11-1-1-1-11111111-111-111111111111-111111-1-1111-1-1-1-11-1-1-1-1-1-1-1
χ411111111-111111111-1-111-1-1111-1-1-1-1-1-1-1111111-111-11-1-1111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-111
χ51111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i321111111111111−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i321−1−i32−1+i32
χ61111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i321-1-111-1-111111-1−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11-1-11+i321−i321−1−i32−1+i321+i321−i321+i321+i321−i321−i321−1−i32−1+i32−1−i32−1+i32-1−1−i32−1+i32-11+i321−i32−1−i32−1−i32−1+i32−1+i321-1-11+i321−i3211+i321−i32
χ71111−1−i32−1+i32−1−i32−1+i32-1111−1−i32−1+i32−1−i32−1+i321111111111-1-111+i321−i32-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-111-1−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1−1−i32−1+i32−1−i32−1+i3211+i321−i321−1−i32−1+i321+i321+i321−i321−i321-1-11+i321−i32-11+i321−i32
χ81111−1−i32−1+i32−1−i32−1+i32-1111−1−i32−1+i32−1−i32−1+i321-1-111-1-1111-1-1-11+i321−i32-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-111-111+i321−i321−1−i32−1+i321+i321−i321+i321+i321−i321−i32-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32-11+i321−i321+i321+i321−i321−i32111−1−i32−1+i32-1−1−i32−1+i32
χ91111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i321111111111111−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i321−1+i32−1−i32
χ101111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i321-1-111-1-111111-1−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11-1-11−i321+i321−1+i32−1−i321−i321+i321−i321−i321+i321+i321−1+i32−1−i32−1+i32−1−i32-1−1+i32−1−i32-11−i321+i32−1+i32−1+i32−1−i32−1−i321-1-11−i321+i3211−i321+i32
χ111111−1+i32−1−i32−1+i32−1−i32-1111−1+i32−1−i32−1+i32−1−i321111111111-1-111−i321+i32-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-111-1−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1−1+i32−1−i32−1+i32−1−i3211−i321+i321−1+i32−1−i321−i321−i321+i321+i321-1-11−i321+i32-11−i321+i32
χ121111−1+i32−1−i32−1+i32−1−i32-1111−1+i32−1−i32−1+i32−1−i321-1-111-1-1111-1-1-11−i321+i32-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-111-111−i321+i321−1+i32−1−i321−i321+i321−i321−i321+i321+i32-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32-11−i321+i321−i321−i321+i321+i32111−1+i32−1−i32-1−1+i32−1−i32
χ1322222222222-12222-1002200-1-1222022-1-122-1-1-1-10020000-1220000002-1-1-1-1022000-1-1-1-1-10000-100
χ1422222222-222-12222-1002200-1-12-2-20-2-21122-1-1-1-10020000-122000000-2-1-1-1-10-2-20001111-10000100
χ152222−1−i3−1+i3−1−i3−1+i3222-1−1−i3−1+i3−1−i3−1+i3-1002200-1-12220−1−i3−1+i3-1-1−1−i3−1+i31+i321−i321+i321−i320020000-1−1−i3−1+i300000021+i321−i321+i321−i320−1−i3−1+i30001+i321+i321−i321−i32-10000-100
χ162222−1−i3−1+i3−1−i3−1+i3-222-1−1−i3−1+i3−1−i3−1+i3-1002200-1-12-2-201+i31−i311−1−i3−1+i31+i321−i321+i321−i320020000-1−1−i3−1+i3000000-21+i321−i321+i321−i3201+i31−i3000−1−i32−1−i32−1+i32−1+i32-10000100
χ172222−1+i3−1−i3−1+i3−1−i3222-1−1+i3−1−i3−1+i3−1−i3-1002200-1-12220−1+i3−1−i3-1-1−1+i3−1−i31−i321+i321−i321+i320020000-1−1+i3−1−i300000021−i321+i321−i321+i320−1+i3−1−i30001−i321−i321+i321+i32-10000-100
χ182222−1+i3−1−i3−1+i3−1−i3-222-1−1+i3−1−i3−1+i3−1−i3-1002200-1-12-2-201−i31+i311−1+i3−1−i31−i321+i321−i321+i320020000-1−1+i3−1−i3000000-21−i321+i321−i321+i3201−i31+i3000−1+i32−1+i32−1−i32−1−i32-10000100
χ1922-1-122220222-1-1-1-1222-1-1-1-1-1-1200-1000022222220-120222-1-122-1-1-1-10-1-1-1-1-100-1-1-10000-10000000
χ2022-1-122220222-1-1-1-12-2-2-1-111-1-120010000222222-20-1-20-2-22-1-1-2-211110-1-1-1-11001110000-10000000
χ2122-1-1−1−i3−1+i3−1−i3−1+i302221+i321−i321+i321−i32222-1-1-1-1-1-1200-10000−1−i3−1+i3−1−i3−1+i3−1−i3−1+i320-120−1−i3−1+i321+i321−i32−1−i3−1+i31+i321+i321−i321−i3201+i321−i321+i321−i32-100-11+i321−i320000-10000000
χ2222-1-1−1−i3−1+i3−1−i3−1+i302221+i321−i321+i321−i322-2-2-1-111-1-120010000−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-20-1-201+i31−i321+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i3201+i321−i321+i321−i321001−1−i32−1+i320000-10000000
χ2322-1-1−1+i3−1−i3−1+i3−1−i302221−i321+i321−i321+i32222-1-1-1-1-1-1200-10000−1+i3−1−i3−1+i3−1−i3−1+i3−1−i320-120−1+i3−1−i321−i321+i32−1+i3−1−i31−i321−i321+i321+i3201−i321+i321−i321+i32-100-11−i321+i320000-10000000
χ2422-1-1−1+i3−1−i3−1+i3−1−i302221−i321+i321−i321+i322-2-2-1-111-1-120010000−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-20-1-201−i31+i321−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i3201−i321+i321−i321+i321001−1+i32−1−i320000-10000000
χ25333300003-1330000333-133333-13-130033000000-13-1-1300-100000000-10000-100-1000000-1-1-100-100
χ26333300003-13300003-3-3-13-3-333-13-1-300330000001-3-11-300-100000000-100001001000000-11100-100
χ2733330000-3-1330000333-133333-1-31300-3-3000000-1-3-1-1-300-10000000010000-100-1000000-11100100
χ2833330000-3-13300003-3-3-13-3-333-1-31-300-3-300000013-11300-100000000100001001000000-1-1-100100
χ293333333333-10333301-13-1-1-100-1-1313300-1-1000011-1-1-1110-1-1-1-1-1-1-1-1-100001-1-1-111000001-1110-1-1
χ303333333333-1033330-113-11100-1-13-13300-1-10000-1-1-111-1-10-1-1111111-10000-1-1-11-1-100000-11-1-1011
χ3133333333-33-10333301-13-1-1-100-11-31-3-300-1-100001-1-1-11110-1-1-1-1-1-1-1-110000111-11100000-11-1-1011
χ3233333333-33-1033330-113-11100-11-3-1-3-300-1-10000-11-11-1-1-10-1-111111110000-1111-1-1000001-1110-1-1
χ333333−3−3i32−3+3i32−3−3i32−3+3i3233-10−3−3i32−3+3i32−3−3i32−3+3i3201-13-1-1-100-1-131−3−3i32−3+3i32001+i321−i32000011-1-1-1−1−i32−1+i3201+i321−i321+i321−i321+i321+i321−i321−i32-1000011+i321−i32-1−1−i32−1+i32000001-1−1−i32−1+i3201+i321−i32
χ343333−3−3i32−3+3i32−3−3i32−3+3i3233-10−3−3i32−3+3i32−3−3i32−3+3i320-113-11100-1-13-1−3−3i32−3+3i32001+i321−i320000-1-1-1111+i321−i3201+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-10000-11+i321−i3211+i321−i3200000-111+i321−i320−1−i32−1+i32
χ353333−3−3i32−3+3i32−3−3i32−3+3i32-33-10−3−3i32−3+3i32−3−3i32−3+3i3201-13-1-1-100-11-313+3i323−3i32001+i321−i3200001-1-1-11−1−i32−1+i3201+i321−i321+i321−i321+i321+i321−i321−i32100001−1−i32−1+i32-1−1−i32−1+i3200000-111+i321−i320−1−i32−1+i32
χ363333−3−3i32−3+3i32−3−3i32−3+3i32-33-10−3−3i32−3+3i32−3−3i32−3+3i320-113-11100-11-3-13+3i323−3i32001+i321−i320000-11-11-11+i321−i3201+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3210000-1−1−i32−1+i3211+i321−i32000001-1−1−i32−1+i3201+i321−i32
χ373333−3+3i32−3−3i32−3+3i32−3−3i3233-10−3+3i32−3−3i32−3+3i32−3−3i3201-13-1-1-100-1-131−3+3i32−3−3i32001−i321+i32000011-1-1-1−1+i32−1−i3201−i321+i321−i321+i321−i321−i321+i321+i32-1000011−i321+i32-1−1+i32−1−i32000001-1−1+i32−1−i3201−i321+i32
χ383333−3+3i32−3−3i32−3+3i32−3−3i3233-10−3+3i32−3−3i32−3+3i32−3−3i320-113-11100-1-13-1−3+3i32−3−3i32001−i321+i320000-1-1-1111−i321+i3201−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-10000-11−i321+i3211−i321+i3200000-111−i321+i320−1+i32−1−i32
χ393333−3+3i32−3−3i32−3+3i32−3−3i32-33-10−3+3i32−3−3i32−3+3i32−3−3i3201-13-1-1-100-11-313−3i323+3i32001−i321+i3200001-1-1-11−1+i32−1−i3201−i321+i321−i321+i321−i321−i321+i321+i32100001−1+i32−1−i32-1−1+i32−1−i3200000-111−i321+i320−1+i32−1−i32
χ403333−3+3i32−3−3i32−3+3i32−3−3i32-33-10−3+3i32−3−3i32−3+3i32−3−3i320-113-11100-11-3-13−3i323+3i32001−i321+i320000-11-11-11−i321+i3201−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3210000-1−1+i32−1−i3211−i321+i32000001-1−1+i32−1−i3201−i321+i32
χ4144-2-24444044-2-2-2-2-2-200-2-200114000000044-2-2-2-200-20000-2-2-200000001111000000000010000000
χ4244-2-2−2−2i3−2+2i3−2−2i3−2+2i3044-21+i31−i31+i31−i3-200-2-2001140000000−2−2i3−2+2i31+i31−i31+i31−i300-20000-21+i31−i30000000−1−i32−1+i32−1−i32−1+i32000000000010000000
χ4344-2-2−2+2i3−2−2i3−2+2i3−2−2i3044-21−i31+i31−i31+i3-200-2-2001140000000−2+2i3−2−2i31−i31+i31−i31+i300-20000-21−i31+i30000000−1+i32−1−i32−1+i32−1−i32000000000010000000
χ44666600006-26-30000-300-2600-3-3-26-2000-3-300000000-20000100000000-20000000000000010000100
χ4566660000-6-26-30000-300-2600-3-3-2-620003300000000-2000010000000020000000000000010000-100
χ4666-3-300000-26600006661-3-3-3-3-3-200-30000000000-201-2000-20000000000000100100000010000000
χ4766-3-300000-26600006-6-61-333-3-3-200300000000002012000-20000000000000-100-100000010000000
χ4866-3-3666606-20-3-3-3-302-2-311100-200-10000-2-20000201-2022011-2-2111100000-1001-1-1000000000000
χ4966-3-3666606-20-3-3-3-30-22-31-1-100-20010000-2-20000-20120-2-201122-1-1-1-100000100-111000000000000
χ5066-3-3−3−3i3−3+3i3−3−3i3−3+3i306-203+3i323−3i323+3i323−3i3202-2-311100-200-100001+i31−i30000201-20−1−i3−1+i30−1−i32−1+i321+i31−i3−1−i32−1−i32−1+i32−1+i3200000-10011+i321−i32000000000000
χ5166-3-3−3−3i3−3+3i3−3−3i3−3+3i306-203+3i323−3i323+3i323−3i320-22-31-1-100-200100001+i31−i30000-201201+i31−i30−1−i32−1+i32−1−i3−1+i31+i321+i321−i321−i3200000100-1−1−i32−1+i32000000000000
χ5266-3-3−3+3i3−3−3i3−3+3i3−3−3i306-203−3i323+3i323−3i323+3i3202-2-311100-200-100001−i31+i30000201-20−1+i3−1−i30−1+i32−1−i321−i31+i3−1+i32−1+i32−1−i32−1−i3200000-10011−i321+i32000000000000
χ5366-3-3−3+3i3−3−3i3−3+3i3−3−3i306-203−3i323+3i323−3i323+3i320-22-31-1-100-200100001−i31+i30000-201201−i31+i30−1+i32−1−i32−1+i3−1−i31−i321−i321+i321+i3200000100-1−1+i32−1−i32000000000000
χ548-88-8-4-4440002-4-444-20000002-2000000−2i32i300-1-11100000000000000000-1-111000000−i3i3−i3i300000000
χ558-88-8-4-4440002-4-444-20000002-20000002i3−2i300-1-11100000000000000000-1-111000000i3−i3i3−i300000000
χ568-88-8-4-444000-4-4-4444000000-44000000000022-2-20000000000000000022-2-2000000000000000000
χ578-88-82+2i32−2i3−2−2i3−2+2i300022+2i32−2i3−2−2i3−2+2i3-20000002-2000000−2i32i3001+i321−i32−1−i32−1+i32000000000000000001+i321−i32−1−i32−1+i32000000−3+i323−i323+i32−3−i3200000000
χ588-88-82+2i32−2i3−2−2i3−2+2i300022+2i32−2i3−2−2i3−2+2i3-20000002-20000002i3−2i3001+i321−i32−1−i32−1+i32000000000000000001+i321−i32−1−i32−1+i320000003−i32−3+i32−3−i323+i3200000000
χ598-88-82+2i32−2i3−2−2i3−2+2i3000-42+2i32−2i3−2−2i3−2+2i34000000-440000000000−1−i3−1+i31+i31−i300000000000000000−1−i3−1+i31+i31−i3000000000000000000
χ608-88-82−2i32+2i3−2+2i3−2−2i300022−2i32+2i3−2+2i3−2−2i3-20000002-2000000−2i32i3001−i321+i32−1+i32−1−i32000000000000000001−i321+i32−1+i32−1−i320000003+i32−3−i32−3+i323−i3200000000
χ618-88-82−2i32+2i3−2+2i3−2−2i300022−2i32+2i3−2+2i3−2−2i3-20000002-20000002i3−2i3001−i321+i32−1+i32−1−i32000000000000000001−i321+i32−1+i32−1−i32000000−3−i323+i323−i32−3+i3200000000
χ628-88-82−2i32+2i3−2+2i3−2−2i3000-42−2i32+2i3−2+2i3−2−2i34000000-440000000000−1+i3−1−i31−i31+i300000000000000000−1+i3−1−i31−i31+i3000000000000000000
χ638-8-44-4-444000-422-2-24000026−262-2000000000022-2-20000000000006−66−60-1-111000000000000000000
χ648-8-44-4-444000-422-2-240000−26262-2000000000022-2-2000000000000−66−660-1-111000000000000000000
χ658-8-442+2i32−2i3−2−2i3−2+2i3000-4−1−i3−1+i31+i31−i34000026−262-20000000000−1−i3−1+i31+i31−i3000000000000−2ζ5−ζ7−ζ13−2ζ232ζ5+ζ7+ζ13+2ζ23ζ5+2ζ7+2ζ13+ζ23−ζ5−2ζ7−2ζ13−ζ2301+i321−i32−1−i32−1+i32000000000000000000
χ668-8-442+2i32−2i3−2−2i3−2+2i3000-4−1−i3−1+i31+i31−i340000−26262-20000000000−1−i3−1+i31+i31−i30000000000002ζ5+ζ7+ζ13+2ζ23−2ζ5−ζ7−ζ13−2ζ23−ζ5−2ζ7−2ζ13−ζ23ζ5+2ζ7+2ζ13+ζ2301+i321−i32−1−i32−1+i32000000000000000000
χ678-8-442−2i32+2i3−2+2i3−2−2i3000-4−1+i3−1−i31−i31+i34000026−262-20000000000−1+i3−1−i31−i31+i3000000000000ζ5+2ζ7+2ζ13+ζ23−ζ5−2ζ7−2ζ13−ζ23−2ζ5−ζ7−ζ13−2ζ232ζ5+ζ7+ζ13+2ζ2301−i321+i32−1+i32−1−i32000000000000000000
χ688-8-442−2i32+2i3−2+2i3−2−2i3000-4−1+i3−1−i31−i31+i340000−26262-20000000000−1+i3−1−i31−i31+i3000000000000−ζ5−2ζ7−2ζ13−ζ23ζ5+2ζ7+2ζ13+ζ232ζ5+ζ7+ζ13+2ζ23−2ζ5−ζ7−ζ13−2ζ2301−i321+i32−1+i32−1−i32000000000000000000
χ69999900009-3-30000003-3-3-3-3-3001-3-330000000000-1311-30000000000010000-10010000000-1100000
χ70999900009-3-3000000-33-3-333001-3-3-300000000001-31-130000000000010000100-100000001-100000
χ7199990000-9-3-30000003-3-3-3-3-30013330000000000-1-311300000000000-10000-100100000001-100000
χ7299990000-9-3-3000000-33-3-33300133-30000000000131-1-300000000000-10000100-10000000-1100000
χ731212-6-600000-412-60000-6002-60033-400000000000000020000200000000000000000000000-10000000
χ7416-16-88-8-888000444-4-4-4000000-220000000000-2-2220000000000000000011-1-1000000000000000000
χ7516-16-884+4i34−4i3−4−4i3−4+4i30004−2−2i3−2+2i32+2i32−2i3-4000000-2200000000001+i31−i3−1−i3−1+i300000000000000000−1−i32−1+i321+i321−i32000000000000000000
χ7616-16-884−4i34+4i3−4+4i3−4−4i30004−2+2i3−2−2i32−2i32+2i3-4000000-2200000000001−i31+i3−1+i3−1−i300000000000000000−1+i32−1−i321−i321+i32000000000000000000
χ771818-9-900000-6-60000006-6333300200-30000000000-20-1200000000000000000100-100000000000000
χ781818-9-900000-6-6000000-6633-3-3002003000000000020-1-200000000000000000-100100000000000000

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