Finite Group Databasebeta

← Group #72220559

Character table — Group #72220559

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11222244444488888888999916161616181818181818181818181818181836363636363636363636363636363636363636363636363636363636363672727272727272728181162162
order12336633366633336666222233662222444444666666666666666666121212121212121212121212121212126666121212122244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ31111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-11111111-1-111-1-111111111-1-11-1-1-1-111-1-1111-1-111-1-11111111111-1-111-1-1-1-1-1-1
χ6111111111111111111111-1-11111111-1-1-1-111-1-1111111-1-11-1-1-1-111-1-11-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ7111111111111111111111-1-111111-1-11111-1-1-1-11111-1-1111-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ8111111111111111111111-1-111111-1-111-1-111111111-1-1111-1-1-1-1-1-1111-1-111-1-11111111111-1-111-1-111-1-1-1-1
χ91-111-1-1111-1-1-11111-1-1-1-111-1-111-1-11-11-1i−ii−ii−i11-1-11-11-111-11-11-11-1-1i−ii−ii−ii−iii−i−iii−i−i1-11-1i−ii−i1-1i−i
χ101-111-1-1111-1-1-11111-1-1-1-111-1-111-1-11-11-1−ii−ii−ii11-1-11-11-111-11-11-11-1-1−ii−ii−ii−ii−i−iii−i−iii1-11-1−ii−ii1-1−ii
χ111-111-1-1111-1-1-11111-1-1-1-111-1-111-1-1-11-11i−ii−i−ii11-1-1-11-1111-11-1-11-11-1i−ii−ii−ii−i−i−iii−i−iii-11-11i−ii−i1-1−ii
χ121-111-1-1111-1-1-11111-1-1-1-111-1-111-1-1-11-11−ii−iii−i11-1-1-11-1111-11-1-11-11-1−ii−ii−ii−iiii−i−iii−i−i-11-11−ii−ii1-1i−i
χ131-111-1-1111-1-1-11111-1-1-1-11-11-111-1-11-1-11i−i−iii−i11-1-11-1-111-11-111-1-11-1i−i−iii−i−iiii−i−iii−i−i1-1-11i−i−ii-11−ii
χ141-111-1-1111-1-1-11111-1-1-1-11-11-111-1-11-1-11−iii−i−ii11-1-11-1-111-11-111-1-11-1−iii−i−iii−i−i−iii−i−iii1-1-11−iii−i-11i−i
χ151-111-1-1111-1-1-11111-1-1-1-11-11-111-1-1-111-1i−i−ii−ii11-1-1-111-11-11-11-111-1-1i−i−iii−i−ii−i−iii−i−iii-111-1i−i−ii-11i−i
χ161-111-1-1111-1-1-11111-1-1-1-11-11-111-1-1-111-1−iii−ii−i11-1-1-111-11-11-11-111-1-1−iii−i−iii−iii−i−iii−i−i-111-1−iii−i-11−ii
χ1722222222222222222222-222-222220000000000-2-2-2-20000-222220000-2000000000000000000000000-2-200
χ1822222222222222222222-2-2-2-222220000000000-2-2-2-20000-2-2-2-2-20000-20000000000000000000000002200
χ19222-12-12-12-1222-12-12-12-12002-1-1-1-100220022222-12-100-1-1-100000022-100-1-100222-12-1-1-1-1-100-1-100-1-10000
χ20222-12-12-12-1222-12-12-12-12002-1-1-1-1002200-2-2-2-22-12-100-1-1-100000022-1001100-2-2-21-21111100-1-100110000
χ21222-12-12-12-1222-12-12-12-12002-1-1-1-100-2-20022-2-22-12-10011-1000000-2-2-100-1-10022-21-211111001100-1-10000
χ22222-12-12-12-1222-12-12-12-12002-1-1-1-100-2-200-2-2222-12-10011-1000000-2-2-1001100-2-22-12-1-1-1-1-1001100110000
χ2322-12-122-12-122-12-12-12-122002-1-1-1-12200220022-12-12-1-100-100002200-1-1-1002200-12-12-1-1-1-1-1-100-1-1000000
χ2422-12-122-12-122-12-12-12-122002-1-1-1-12200-2-200-2-2-12-12-1-100-100002200-11100-2-2001-21-21111-1-10011000000
χ2522-12-122-12-122-12-12-12-122002-1-1-1-1-2-2002200-2-2-12-121100-10000-2-200-1-1-10022001-21-211111100-1-1000000
χ2622-12-122-12-122-12-12-12-122002-1-1-1-1-2-200-2-20022-12-121100-10000-2-200-11100-2-200-12-12-1-1-1-1110011000000
χ272-222-2-2222-2-2-22222-2-2-2-2-22-2222-2-20000000000-2-2220000-22-22-200002000000000000000000000000-2200
χ282-222-2-2222-2-2-22222-2-2-2-2-2-22222-2-20000000000-2-2220000-2-22-22000020000000000000000000000002-200
χ292-22-1-212-121-2-22-12-1-21-21200-2-1-111002-2002i−2i2i−2i2-1-2100-11-10000002-2100−ii002i−2i2i−i−2ii−i−iii00-1100−ii0000
χ302-22-1-212-121-2-22-12-1-21-21200-2-1-111002-200−2i2i−2i2i2-1-2100-11-10000002-2100i−i00−2i2i−2ii2i−iii−i−i00-1100i−i0000
χ312-22-1-212-121-2-22-12-1-21-21200-2-1-11100-22002i−2i−2i2i2-1-21001-1-1000000-22100−ii002i−2i−2ii2i−iii−i−i001-100−ii0000
χ322-22-1-212-121-2-22-12-1-21-21200-2-1-11100-2200−2i2i2i−2i2-1-21001-1-1000000-22100i−i00−2i2i2i−i−2ii−i−iii001-100i−i0000
χ332-2-121-22-121-2-2-12-121-21-2200-2-1-1112-2002i−2i002i−2i-121-2-1100-100002-2001−ii002i−2i00−i2ii−2i−i−iii-1100−ii000000
χ342-2-121-22-121-2-2-12-121-21-2200-2-1-1112-200−2i2i00−2i2i-121-2-1100-100002-2001i−i00−2i2i00i−2i−i2iii−i−i-1100i−i000000
χ352-2-121-22-121-2-2-12-121-21-2200-2-1-111-22002i−2i00−2i2i-121-21-100-10000-22001−ii002i−2i00i−2i−i2iii−i−i1-100−ii000000
χ362-2-121-22-121-2-2-12-121-21-2200-2-1-111-2200−2i2i002i−2i-121-21-100-10000-22001i−i00−2i2i00−i2ii−2i−i−iii1-100i−i000000
χ3744444414-24-2111-2-2-2-21104401-21-2000022220000000000011-2-2000002222-1-1-1-1000000000000-1-1-1-10000
χ3844444414-24-2111-2-2-2-21104401-21-20000-2-2-2-20000000000011-2-200000-2-2-2-2111100000000000011110000
χ3944444414-24-2111-2-2-2-2110-4-401-21-2000022-2-200000000000-1-1220000022-2-2-1-111000000000000-1-1110000
χ4044444414-24-2111-2-2-2-2110-4-401-21-20000-2-22200000000000-1-12200000-2-22211-1-100000000000011-1-10000
χ41444444-24141-2-2-21111-2-20440-21-212222000000000022220-2-211-1-1-1-100000000000000000-1-1-1-100000000
χ42444444-24141-2-2-21111-2-20440-21-21-2-2-2-20000000000-2-2-2-20-2-211111100000000000000000111100000000
χ43444444-24141-2-2-21111-2-20-4-40-21-2122-2-2000000000022-2-2022-1-1-1-11100000000000000000-1-11100000000
χ44444444-24141-2-2-21111-2-20-4-40-21-21-2-2220000000000-2-222022-1-111-1-10000000000000000011-1-100000000
χ45444-24-24-24-2444-24-24-24-2-400-4-2-2-2-20000000000-42-42000020000000020000000000000000000000000000
χ4644-24-244-24-244-24-24-24-24-400-4-2-2-2-200000000002-42-4000020000000020000000000000000000000000000
χ4744-2-2-2-2414144-2-2-2-2-2-2-2-2400411110000000044-2-2-2-20000100000000100000000-2-2-2-21111000000000000
χ4844-2-2-2-2414144-2-2-2-2-2-2-2-24004111100000000-4-4-2-2-2-200001000000001000000002222-1-1-1-1000000000000
χ4944-2-2-2-2414144-2-2-2-2-2-2-2-2-400-41111000000000022220000-100000000-10000000000003i−3i3i−3i000000000000
χ5044-2-2-2-2414144-2-2-2-2-2-2-2-2-400-41111000000000022220000-100000000-1000000000000−3i3i−3i3i000000000000
χ514-444-4-414-2-42-111-2-222-1-104-401-2-1200002i−2i2i−2i000000000001-1-22000002i−2i2i−2i−ii−ii000000000000−ii−ii0000
χ524-444-4-414-2-42-111-2-222-1-104-401-2-120000−2i2i−2i2i000000000001-1-2200000−2i2i−2i2ii−ii−i000000000000i−ii−i0000
χ534-444-4-414-2-42-111-2-222-1-10-4401-2-1200002i−2i−2i2i00000000000-112-2000002i−2i−2i2i−iii−i000000000000−iii−i0000
χ544-444-4-414-2-42-111-2-222-1-10-4401-2-120000−2i2i2i−2i00000000000-112-200000−2i2i2i−2ii−i−ii000000000000i−i−ii0000
χ554-444-4-4-241-4-12-2-211-1-12204-40-212-12-22-200000000002-22-20-221-1-11-1100000000000000000-11-1100000000
χ564-444-4-4-241-4-12-2-211-1-12204-40-212-1-22-220000000000-22-220-221-11-11-1000000000000000001-11-100000000
χ574-444-4-4-241-4-12-2-211-1-1220-440-212-12-2-2200000000002-2-2202-2-11-111-100000000000000000-111-100000000
χ584-444-4-4-241-4-12-2-211-1-1220-440-212-1-222-20000000000-222-202-2-111-1-11000000000000000001-1-1100000000
χ594-44-2-424-242-4-44-24-2-42-42-4004-2-2220000000000-424-20000200000000-20000000000000000000000000000
χ604-4-242-44-242-4-4-24-242-42-4-4004-2-22200000000002-4-240000200000000-20000000000000000000000000000
χ614-4-2-222414-1-4-4-2-2-2-22222400-411-1-1000000004i−4i-2-2220000100000000-100000000−2i−2i2i2iii−i−i000000000000
χ624-4-2-222414-1-4-4-2-2-2-22222400-411-1-100000000−4i4i-2-2220000100000000-1000000002i2i−2i−2i−i−iii000000000000
χ634-4-2-222414-1-4-4-2-2-2-22222-400411-1-1000000000022-2-20000-10000000010000000000003-3-33000000000000
χ644-4-2-222414-1-4-4-2-2-2-22222-400411-1-1000000000022-2-20000-1000000001000000000000-333-3000000000000
χ65888-48-42-4-4-4-422-1-42-422-10000-12-12000000440000000000000000000000-2-200-2-200000000000000110000
χ66888-48-42-4-4-4-422-1-42-422-10000-12-12000000-4-4000000000000000000000022002200000000000000-1-10000
χ67888-48-4-4-42-42-4-422-12-1-4200002-12-10044000000000000-2-20000000-2-200000000000000000001100000000
χ68888-48-4-4-42-42-4-422-12-1-4200002-12-100-4-4000000000000220000000220000000000000000000-1-100000000
χ6988-48-482-4-4-4-42-122-42-4-120000-12-120000440000000000000000000000-2-200-2-20000000000000011000000
χ7088-48-482-4-4-4-42-122-42-4-120000-12-120000-4-4000000000000000000000022002200000000000000-1-1000000
χ7188-48-48-4-42-42-42-4-12-122-400002-12-144000000000000-2-20000000-2-20000000000000000000110000000000
χ7288-48-48-4-42-42-42-4-12-122-400002-12-1-4-4000000000000220000000220000000000000000000-1-10000000000
χ738-88-4-842-4-444-22-1-424-2-210000-121-20000004i−4i0000000000000000000000−2i2i00−2i2i00000000000000i−i0000
χ748-88-4-842-4-444-22-1-424-2-210000-121-2000000−4i4i00000000000000000000002i−2i002i−2i00000000000000−ii0000
χ758-88-4-84-4-424-24-422-1-214-200002-1-21004-4000000000000-220000000-2200000000000000000001-100000000
χ768-88-4-84-4-424-24-422-1-214-200002-1-2100-440000000000002-200000002-20000000000000000000-1100000000
χ778-8-484-82-4-444-2-122-4-241-20000-121-200004i−4i0000000000000000000000−2i2i00−2i2i00000000000000i−i000000
χ788-8-484-82-4-444-2-122-4-241-20000-121-20000−4i4i00000000000000000000002i−2i002i−2i00000000000000−ii000000
χ798-8-484-8-4-424-242-4-121-2-2400002-1-214-4000000000000-220000000-2200000000000000000001-10000000000
χ808-8-484-8-4-424-242-4-121-2-2400002-1-21-440000000000002-200000002-20000000000000000000-110000000000
χ811616-8-8-8-844-84-84-2-24444-2-200001-21-200000000000000000000000000000000000000000000000000000000
χ821616-8-8-8-8-84444-844-2-2-2-2440000-21-2100000000000000000000000000000000000000000000000000000000
χ8316-16-8-88844-8-48-4-2-244-4-42200001-2-1200000000000000000000000000000000000000000000000000000000
χ8416-16-8-888-844-4-4844-2-222-4-40000-212-100000000000000000000000000000000000000000000000000000000

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