Finite Group Databasebeta

← Group #72220708

Character table — Group #72220708

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112222444444668888888888889999121212121212121212121616181818181818181824242424242424243636363636363636363636363636545454545454727272728181108108108108108108
order123366333666443333336666662222121212121212121212123622226666121212121212121266666666666666444444666622121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111-1-1111111111111111-1-111111111111111-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-1
χ4111111111111111111111111111-1-11111111111111-1-111111111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111
χ5111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ6111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-11111
χ7111111111111-1-11111111111111-1-11-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111
χ8111111111111-1-11111111111111-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1
χ91-111-1-1111-1-1-1i−i111111-1-1-1-1-1-111-1-1ii−i−iii−i−ii−i1-11-11-111-1-1iiii−i−i−i−i1-11-11-11-11-11-11-1i−ii−ii−i1-11-11-1i−ii−ii−i
χ101-111-1-1111-1-1-1i−i111111-1-1-1-1-1-111-1-1ii−i−iii−i−ii−i1-1-11-1111-1-1iiii−i−i−i−i-11-111-11-11-1-11-11i−i−ii−ii-11-111-1i−i−ii−ii
χ111-111-1-1111-1-1-1i−i111111-1-1-1-1-1-11-11-1ii−i−iii−i−ii−i1-11-1-1111-1-1iiii−i−i−i−i1-1-111-1-11-111-1-11−iii−i−ii1-1-11-11−iii−i−ii
χ121-111-1-1111-1-1-1i−i111111-1-1-1-1-1-11-11-1ii−i−iii−i−ii−i1-1-111-111-1-1iiii−i−i−i−i-111-11-1-11-11-111-1−ii−iii−i-111-1-11−ii−iii−i
χ131-111-1-1111-1-1-1−ii111111-1-1-1-1-1-111-1-1−i−iii−i−iii−ii1-11-11-111-1-1−i−i−i−iiiii1-11-11-11-11-11-11-1−ii−ii−ii1-11-11-1−ii−ii−ii
χ141-111-1-1111-1-1-1−ii111111-1-1-1-1-1-111-1-1−i−iii−i−iii−ii1-1-11-1111-1-1−i−i−i−iiiii-11-111-11-11-1-11-11−iii−ii−i-11-111-1−iii−ii−i
χ151-111-1-1111-1-1-1−ii111111-1-1-1-1-1-11-11-1−i−iii−i−iii−ii1-11-1-1111-1-1−i−i−i−iiiii1-1-111-1-11-111-1-11i−i−iii−i1-1-11-11i−i−iii−i
χ161-111-1-1111-1-1-1−ii111111-1-1-1-1-1-11-11-1−i−iii−i−iii−ii1-1-111-111-1-1−i−i−i−iiiii-111-11-1-11-11-111-1i−ii−i−ii-111-1-11i−ii−i−ii
χ1722222222222200222222222222-222-20000000000220000-2-2-2-2000000000000-2-2222200000000000000-2-2000000
χ1822222222222200222222222222-2-2-2-20000000000220000-2-2-2-2000000000000-2-2-2-2-2-20000000000000022000000
χ19222-12-12-122-12222-1-1-12-12-12-1-1-120022-12-1-1-1-1-122-1-100222-12-12-1-1-12-1-1-100-1-1-1-10000002200002200-1-1000000-1-1
χ20222-12-12-122-12222-1-1-12-12-12-1-1-120022-12-1-1-1-1-122-1-100-2-22-12-12-1-1-12-1-1-10011-1-1000000-2-20000-2-2001100000011
χ21222-12-12-122-12-2-22-1-1-12-12-12-1-1-12002-21-211111-2-2-1-100222-12-1-2111-211100-1-1-1-1000000220000-2-200-1-100000011
χ22222-12-12-122-12-2-22-1-1-12-12-12-1-1-12002-21-211111-2-2-1-100-2-22-12-1-2111-21110011-1-1000000-2-20000220011000000-1-1
χ2322-12-122-122-1222-12-1-1-12-12-12-1-12002-12-12-1-1-1-122-1-12200-12-12-12-1-1-12-1-1-1-100-1-100002200002200-1-1000000-1-100
χ2422-12-122-122-1222-12-1-1-12-12-12-1-12002-12-12-1-1-1-122-1-1-2-200-12-12-12-1-1-12-1-11100-1-10000-2-20000-2-200110000001100
χ2522-12-122-122-12-2-2-12-1-1-12-12-12-1-120021-21-21111-2-2-1-12200-12-121-2111-211-1-100-1-10000220000-2-200-1-10000001100
χ2622-12-122-122-12-2-2-12-1-1-12-12-12-1-120021-21-21111-2-2-1-1-2-200-12-121-2111-2111100-1-10000-2-20000220011000000-1-100
χ272-222-2-2222-2-2-200222222-2-2-2-2-2-2-22-2200000000002-20000-2-222000000000000-222-22-200000000000000-22000000
χ282-222-2-2222-2-2-200222222-2-2-2-2-2-2-2-22200000000002-20000-2-222000000000000-22-22-22000000000000002-2000000
χ292-22-1-212-12-21-22i−2i2-1-1-12-1-21-2111200-22i−i−2ii−i−iii2i−2i-11002-22-1-212i−i−i−i−2iiii00-11-110000002-200002i−2i00-11000000−ii
χ302-22-1-212-12-21-22i−2i2-1-1-12-1-21-2111200-22i−i−2ii−i−iii2i−2i-1100-222-1-212i−i−i−i−2iiii001-1-11000000-220000−2i2i001-1000000i−i
χ312-22-1-212-12-21-2−2i2i2-1-1-12-1-21-2111200-2−2ii2i−iii−i−i−2i2i-11002-22-1-21−2iiii2i−i−i−i00-11-110000002-20000−2i2i00-11000000i−i
χ322-22-1-212-12-21-2−2i2i2-1-1-12-1-21-2111200-2−2ii2i−iii−i−i−2i2i-1100-222-1-21−2iiii2i−i−i−i001-1-11000000-2200002i−2i001-1000000−ii
χ332-2-121-22-12-21-22i−2i-12-1-1-121-21-211200-2−i2ii−2i−i−iii2i−2i-112-200-121-2−i2i−i−ii−2iii-1100-1100002-200002i−2i00-11000000−ii00
χ342-2-121-22-12-21-22i−2i-12-1-1-121-21-211200-2−i2ii−2i−i−iii2i−2i-11-2200-121-2−i2i−i−ii−2iii1-100-110000-220000−2i2i001-1000000i−i00
χ352-2-121-22-12-21-2−2i2i-12-1-1-121-21-211200-2i−2i−i2iii−i−i−2i2i-112-200-121-2i−2iii−i2i−i−i-1100-1100002-20000−2i2i00-11000000i−i00
χ362-2-121-22-12-21-2−2i2i-12-1-1-121-21-211200-2i−2i−i2iii−i−i−2i2i-11-2200-121-2i−2iii−i2i−i−i1-100-110000-2200002i−2i001-1000000−ii00
χ3744444414-2-241221111-2-2-2-21111044022222222-1-1-2-200000000-1-1-1-1-1-1-1-100000011-2-20000220000000000-1-10000
χ3844444414-2-241221111-2-2-2-211110-4-4022222222-1-1-2-200000000-1-1-1-1-1-1-1-1000000-1-1220000-2-20000000000110000
χ3944444414-2-241-2-21111-2-2-2-211110440-2-2-2-2-2-2-2-211-2-2000000001111111100000011-2-20000-2-20000000000110000
χ4044444414-2-241-2-21111-2-2-2-211110-4-40-2-2-2-2-2-2-2-211-2-20000000011111111000000-1-1220000220000000000-1-10000
χ41444444-24114-200-2-2-2-21111-2-2-2-204400000000000112222000000000000222200-2-211-1-1-1-1000000-1-1-1-100000000
χ42444444-24114-200-2-2-2-21111-2-2-2-20440000000000011-2-2-2-2000000000000-2-2-2-200-2-2111111000000111100000000
χ43444444-24114-200-2-2-2-21111-2-2-2-20-4-4000000000001122-2-200000000000022-2-20022-1-1-1-111000000-1-11100000000
χ44444444-24114-200-2-2-2-21111-2-2-2-20-4-40000000000011-2-222000000000000-2-2220022-1-111-1-100000011-1-100000000
χ45444-24-24-244-24004-2-2-24-24-24-2-2-2-400-40000000000-2-20000-42-420000000000002200000000000000000000000000
χ4644-24-244-244-2400-24-2-2-24-24-24-2-2-400-40000000000-2-200002-42-40000000000002200000000000000000000000000
χ4744-2-2-2-241441400-2-211-2-2-2-2-2-211-400-400003-33-3001100002222003-3003-30000-1-100000000000000000000000000
χ4844-2-2-2-241441400-2-211-2-2-2-2-2-211-400-40000-33-3300110000222200-3300-330000-1-100000000000000000000000000
χ4944-2-2-2-241441444-2-211-2-2-2-2-2-2114004-2-2-2-2111144110000-2-2-2-2-2-211-2-21100001100000000000000000000000000
χ5044-2-2-2-2414414-4-4-2-211-2-2-2-2-2-21140042222-1-1-1-1-4-4110000-2-2-2-222-1-122-1-100001100000000000000000000000000
χ514-444-4-414-22-4-12i−2i1111-2-222-1-1-1-104-402i2i−2i−2i2i2i−2i−2i−ii-2200000000−i−i−i−iiiii0000001-1-2200002i−2i0000000000−ii0000
χ524-444-4-414-22-4-12i−2i1111-2-222-1-1-1-10-4402i2i−2i−2i2i2i−2i−2i−ii-2200000000−i−i−i−iiiii000000-112-20000−2i2i0000000000i−i0000
χ534-444-4-414-22-4-1−2i2i1111-2-222-1-1-1-104-40−2i−2i2i2i−2i−2i2i2ii−i-2200000000iiii−i−i−i−i0000001-1-220000−2i2i0000000000i−i0000
χ544-444-4-414-22-4-1−2i2i1111-2-222-1-1-1-10-440−2i−2i2i2i−2i−2i2i2ii−i-2200000000iiii−i−i−i−i000000-112-200002i−2i0000000000−ii0000
χ554-444-4-4-241-1-4200-2-2-2-211-1-1222204-4000000000001-12-22-20000000000002-22-200-221-1-11-11000000-11-1100000000
χ564-444-4-4-241-1-4200-2-2-2-211-1-1222204-4000000000001-1-22-22000000000000-22-2200-221-11-11-10000001-11-100000000
χ574-444-4-4-241-1-4200-2-2-2-211-1-122220-44000000000001-12-2-220000000000002-2-22002-2-11-111-1000000-111-100000000
χ584-444-4-4-241-1-4200-2-2-2-211-1-122220-44000000000001-1-222-2000000000000-222-2002-2-111-1-110000001-1-1100000000
χ594-44-2-424-24-42-4004-2-2-24-2-42-4222-40040000000000-220000-424-20000000000002-200000000000000000000000000
χ604-4-242-44-24-42-400-24-2-2-242-42-422-40040000000000-2200002-4-240000000000002-200000000000000000000000000
χ614-4-2-222414-4-1-400-2-211-2-22222-1-1-400400003i−3i−3i3i001-1000022-2-2003i−3i00−3i3i0000-1100000000000000000000000000
χ624-4-2-222414-4-1-400-2-211-2-22222-1-1-40040000−3i3i3i−3i001-1000022-2-200−3i3i003i−3i0000-1100000000000000000000000000
χ634-4-2-222414-4-1-44i−4i-2-211-2-22222-1-1400-4−2i−2i2i2iii−i−i4i−4i1-10000-2-222−2i−2iii2i2i−i−i00001-100000000000000000000000000
χ644-4-2-222414-4-1-4−4i4i-2-211-2-22222-1-1400-42i2i−2i−2i−i−iii−4i4i1-10000-2-2222i2i−i−i−2i−2iii00001-100000000000000000000000000
χ65888-48-42-4-4-4-42442-1-1-1-42-422-1-1-100004-24-2-2-2-2-2-2-22200000000-2111-211100000000000000000000000000000000
χ66888-48-42-4-4-4-42-4-42-1-1-1-42-422-1-1-10000-42-4222222222000000002-1-1-12-1-1-100000000000000000000000000000000
χ67888-48-4-4-422-4-400-42222-12-1-422200000000000000-1-1004400000000000000-2-200000000-2-2000000001100000000
χ68888-48-4-4-422-4-400-42222-12-1-422200000000000000-1-100-4-40000000000000022000000002200000000-1-100000000
χ6988-48-482-4-4-4-4244-12-1-12-42-4-12-1-10000-24-24-2-2-2-2-2-222000000001-2111-21100000000000000000000000000000000
χ7088-48-482-4-4-4-42-4-4-12-1-12-42-4-12-1-100002-42-42222222200000000-12-1-1-12-1-100000000000000000000000000000000
χ7188-48-48-4-422-4-4002-422-12-122-42200000000000000-1-14400000000000000-2-200000000-2-200000000110000000000
χ7288-48-48-4-422-4-4002-422-12-122-42200000000000000-1-1-4-40000000000000022000000002200000000-1-10000000000
χ7388-4-4-4-422-4-42244-1-15-42222-1-15-40000-2-2-2-24-24-2-2-2-1-10000000011-2111-2100000000000000000000000000000000
χ7488-4-4-4-422-4-42244-1-1-452222-1-1-450000-2-2-2-2-24-24-2-2-1-100000000111-2111-200000000000000000000000000000000
χ7588-4-4-4-422-4-422-4-4-1-15-42222-1-15-400002222-42-4222-1-100000000-1-12-1-1-12-100000000000000000000000000000000
χ7688-4-4-4-422-4-422-4-4-1-1-452222-1-1-45000022222-42-422-1-100000000-1-1-12-1-1-1200000000000000000000000000000000
χ778-88-4-842-4-444-24i−4i2-1-1-1-424-2-211100004i−2i−4i2i−2i−2i2i2i−2i2i2-200000000−2iiii2i−i−i−i00000000000000000000000000000000
χ788-88-4-842-4-444-2−4i4i2-1-1-1-424-2-21110000−4i2i4i−2i2i2i−2i−2i2i−2i2-2000000002i−i−i−i−2iiii00000000000000000000000000000000
χ798-88-4-84-4-42-24400-42222-1-214-2-2-200000000000000-11004-400000000000000-2200000000-22000000001-100000000
χ808-88-4-84-4-42-24400-42222-1-214-2-2-200000000000000-1100-44000000000000002-2000000002-200000000-1100000000
χ818-8-484-82-4-444-24i−4i-12-1-12-4-241-2110000−2i4i2i−4i−2i−2i2i2i−2i2i2-200000000i−2iii−i2i−i−i00000000000000000000000000000000
χ828-8-484-82-4-444-2−4i4i-12-1-12-4-241-21100002i−4i−2i4i2i2i−2i−2i2i−2i2-200000000−i2i−i−ii−2iii00000000000000000000000000000000
χ838-8-484-8-4-42-244002-422-121-2-24-2-200000000000000-114-400000000000000-2200000000-22000000001-10000000000
χ848-8-484-8-4-42-244002-422-121-2-24-2-200000000000000-11-44000000000000002-2000000002-200000000-110000000000
χ858-8-4-44422-44-2-24i−4i-1-15-422-2-211-540000−2i−2i2i2i4i−2i−4i2i−2i2i-1100000000ii−2ii−i−i2i−i00000000000000000000000000000000
χ868-8-4-44422-44-2-24i−4i-1-1-4522-2-2114-50000−2i−2i2i2i−2i4i2i−4i−2i2i-1100000000iii−2i−i−i−i2i00000000000000000000000000000000
χ878-8-4-44422-44-2-2−4i4i-1-15-422-2-211-5400002i2i−2i−2i−4i2i4i−2i2i−2i-1100000000−i−i2i−iii−2ii00000000000000000000000000000000
χ888-8-4-44422-44-2-2−4i4i-1-1-4522-2-2114-500002i2i−2i−2i2i−4i−2i4i2i−2i-1100000000−i−i−i2iiii−2i00000000000000000000000000000000
χ891616-8-8-8-8-84444-80044-2-2-2-2-2-244-2-20000000000000011000000000000000000000000000000000000000000000000
χ9016-16-8-888-844-4-480044-2-2-2-222-4-422000000000000001-1000000000000000000000000000000000000000000000000

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