Finite Group Databasebeta

← Group #13165412

Character table — Group #13165412

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122224444444466888888889999121212121212121212121212181818181818181824242424242424242424242424242424363636363636363654545454545472727272
order122236663366666644336666662222222266666666444466666666666666661212121244441212121244444412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1
χ3111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-111
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1
χ51111111111111111-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111-1-111111111111111-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1111111111111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1
χ81111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ911-1-111-1-11111-1-1-1-1i−i1111-1-1-1-11-11-11-11-111-1-111-1-111-1-11-1-111-11-111-1-111-1-1ii−i−ii−ii−i11-1-1i−iii−i−ii−ii−i
χ1011-1-111-1-11111-1-1-1-1i−i1111-1-1-1-11-11-11-1-1111-1-1-1-111-1-1111-1-111-1-1111-1-1-1-111ii−i−ii−i−ii-1-111i−i−i−iiii−i−ii
χ1111-1-111-1-11111-1-1-1-1i−i1111-1-1-1-11-11-1-111-1-1-11111-1-1-1-1111-1-11-111-1-1-11111-1-1ii−i−i−iii−i-1-111i−i−i−iii−iii−i
χ1211-1-111-1-11111-1-1-1-1i−i1111-1-1-1-11-11-1-11-11-1-111-1-11111-1-11-1-11-11-11-1-111-1-111ii−i−i−ii−ii11-1-1i−iii−i−i−ii−ii
χ1311-1-111-1-11111-1-1-1-1−ii1111-1-1-1-11-11-11-11-111-1-111-1-111-1-11-1-111-11-111-1-111-1-1−i−iii−ii−ii11-1-1−ii−i−iii−ii−ii
χ1411-1-111-1-11111-1-1-1-1−ii1111-1-1-1-11-11-11-1-1111-1-1-1-111-1-1111-1-111-1-1111-1-1-1-111−i−iii−iii−i-1-111−iiii−i−i−iii−i
χ1511-1-111-1-11111-1-1-1-1−ii1111-1-1-1-11-11-1-111-1-1-11111-1-1-1-1111-1-11-111-1-1-11111-1-1−i−iiii−i−ii-1-111−iiii−i−ii−i−ii
χ1611-1-111-1-11111-1-1-1-1−ii1111-1-1-1-11-11-1-11-11-1-111-1-11111-1-11-1-11-11-11-1-111-1-111−i−iiii−ii−i11-1-1−ii−i−iiii−ii−i
χ1722222222222222222222222222-2-2-2-20000000000000000-2-2-2-2000000000000222200000000-2-200000000
χ182222222222222222-2-222222222-2-2-2-20000000000000000-2-2-2-2000000000000-2-2-2-2000000002200000000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-100000000-1-1-1-10000000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-1222222-2-2-1-1-1-11111-2-2-2-2-1-1-1-122-2-2-1-1-1-111110000000011110000000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-12222-2-2221111-1-1-1-1-2-2-2-2-1-1-1-1-2-2221111-1-1-1-10000000011110000000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-12222-2-2-2-2111111112222-1-1-1-1-2-2-2-21111111100000000-1-1-1-10000000000
χ2322-2-222-2-22222-2-2-2-22i−2i2222-2-2-2-2-22-220000000000000000-222-20000000000002i2i−2i−2i00000000−2i2i00000000
χ2422-2-222-2-22222-2-2-2-2−2i2i2222-2-2-2-2-22-220000000000000000-222-2000000000000−2i−2i2i2i000000002i−2i00000000
χ2522-2-2-1-1112222-2-2-2-200-1-1-1-111112-22-22-22-2-1-111-1-11122-2-2-111-12-22-2-1-111-1-11100000000-1-1110000000000
χ2622-2-2-1-1112222-2-2-2-200-1-1-1-111112-22-22-2-22-1-11111-1-1-2-222-111-12-2-22-1-11111-1-10000000011-1-10000000000
χ2722-2-2-1-1112222-2-2-2-200-1-1-1-111112-22-2-222-211-1-1-1-111-2-222-111-1-222-211-1-1-1-1110000000011-1-10000000000
χ2822-2-2-1-1112222-2-2-2-200-1-1-1-111112-22-2-22-2211-1-111-1-122-2-2-111-1-22-2211-1-111-1-100000000-1-1110000000000
χ292-22-22-22-222-2-222-2-20022-2-222-2-222-2-2000000000000000022-2-2000000000000000000000000002i−2i2i−2i0000
χ302-22-22-22-222-2-222-2-20022-2-222-2-222-2-2000000000000000022-2-200000000000000000000000000−2i2i−2i2i0000
χ312-22-22-22-222-2-222-2-20022-2-222-2-2-2-2220000000000002-22-2-2-222000000000000000000002-22-20000000000
χ322-22-22-22-222-2-222-2-20022-2-222-2-2-2-222000000000000-22-22-2-22200000000000000000000-22-220000000000
χ332-22-2-11-1122-2-222-2-200-1-111-1-111-2-2220000−i3i3−i3i3−i3i3−i3i32-22-211-1-10000−i3i3−i3i3−i3i3−i3i300000000-11-110000000000
χ342-22-2-11-1122-2-222-2-200-1-111-1-111-2-2220000−i3i3−i3i3i3−i3i3−i3-22-2211-1-10000−i3i3−i3i3i3−i3i3−i3000000001-11-10000000000
χ352-22-2-11-1122-2-222-2-200-1-111-1-111-2-2220000i3−i3i3−i3−i3i3−i3i3-22-2211-1-10000i3−i3i3−i3−i3i3−i3i3000000001-11-10000000000
χ362-22-2-11-1122-2-222-2-200-1-111-1-111-2-2220000i3−i3i3−i3i3−i3i3−i32-22-211-1-10000i3−i3i3−i3i3−i3i3−i300000000-11-110000000000
χ372-2-222-2-2222-2-2-2-2220022-2-2-2-2222-2-2200000000000000002-22-2000000000000000000000000002-2-220000
χ382-2-222-2-2222-2-2-2-2220022-2-2-2-2222-2-2200000000000000002-22-200000000000000000000000000-222-20000
χ392-2-222-2-2222-2-2-2-2220022-2-2-2-222-222-20000000000002-2-22-22-22000000000000000000002-2-220000000000
χ402-2-222-2-2222-2-2-2-2220022-2-2-2-222-222-2000000000000-222-2-22-2200000000000000000000-222-20000000000
χ412-2-22-111-122-2-2-2-22200-1-11111-1-1-222-20000−i3i3i3−i3−i3i3i3−i32-2-221-11-10000−i3i3i3−i3−i3i3i3−i300000000-111-10000000000
χ422-2-22-111-122-2-2-2-22200-1-11111-1-1-222-20000−i3i3i3−i3i3−i3−i3i3-222-21-11-10000−i3i3i3−i3i3−i3−i3i3000000001-1-110000000000
χ432-2-22-111-122-2-2-2-22200-1-11111-1-1-222-20000i3−i3−i3i3−i3i3i3−i3-222-21-11-10000i3−i3−i3i3−i3i3i3−i3000000001-1-110000000000
χ442-2-22-111-122-2-2-2-22200-1-11111-1-1-222-20000i3−i3−i3i3i3−i3−i3i32-2-221-11-10000i3−i3−i3i3i3−i3−i3i300000000-111-10000000000
χ45444444441-21-21-21-2441-21-21-21-200000022000022220000000000-1-10000-1-1-1-11-21-20022000000000000-1-1
χ46444444441-21-21-21-2441-21-21-21-2000000-2-20000-2-2-2-2000000000011000011111-21-200-2-200000000000011
χ47444444441-21-21-21-2-4-41-21-21-21-200000022000022220000000000-1-10000-1-1-1-1-12-1200-2-200000000000011
χ48444444441-21-21-21-2-4-41-21-21-21-2000000-2-20000-2-2-2-200000000001100001111-12-120022000000000000-1-1
χ4944444444-21-21-21-2144-21-21-21-21000022002222000000000000-1-100-1-1-1-10000-21-2122000000000000-1-100
χ5044444444-21-21-21-2144-21-21-21-210000-2-200-2-2-2-2000000000000110011110000-21-21-2-20000000000001100
χ5144444444-21-21-21-21-4-4-21-21-21-21000022002222000000000000-1-100-1-1-1-100002-12-1-2-20000000000001100
χ5244444444-21-21-21-21-4-4-21-21-21-210000-2-200-2-2-2-20000000000001100111100002-12-122000000000000-1-100
χ534444-2-2-2-24444444400-2-2-2-2-2-2-2-2-4-4-4-4000000000000000022220000000000000000000000000000000000
χ5444-4-444-4-41-21-2-12-124i−4i1-21-2-12-120000002-2000022-2-20000000000-110000-1-111i−2i−i2i002i−2i000000000000−ii
χ5544-4-444-4-41-21-2-12-124i−4i1-21-2-12-12000000-220000-2-22200000000001-1000011-1-1i−2i−i2i00−2i2i000000000000i−i
χ5644-4-444-4-41-21-2-12-12−4i4i1-21-2-12-120000002-2000022-2-20000000000-110000-1-111−i2ii−2i00−2i2i000000000000i−i
χ5744-4-444-4-41-21-2-12-12−4i4i1-21-2-12-12000000-220000-2-22200000000001-1000011-1-1−i2ii−2i002i−2i000000000000−ii
χ5844-4-444-4-4-21-212-12-14i−4i-21-212-12-100002-20022-2-2000000000000-1100-1-1110000−2ii2i−i2i−2i000000000000−ii00
χ5944-4-444-4-4-21-212-12-14i−4i-21-212-12-10000-2200-2-2220000000000001-10011-1-10000−2ii2i−i−2i2i000000000000i−i00
χ6044-4-444-4-4-21-212-12-1−4i4i-21-212-12-100002-20022-2-2000000000000-1100-1-11100002i−i−2ii−2i2i000000000000i−i00
χ6144-4-444-4-4-21-212-12-1−4i4i-21-212-12-10000-2200-2-2220000000000001-10011-1-100002i−i−2ii2i−2i000000000000−ii00
χ6244-4-4-2-2224444-4-4-4-400-2-2-2-22222-44-4400000000000000002-2-220000000000000000000000000000000000
χ634-44-4-22-2244-4-444-4-400-2-222-2-22244-4-40000000000000000-2-2220000000000000000000000000000000000
χ644-4-44-222-244-4-4-4-44400-2-22222-2-24-4-440000000000000000-22-220000000000000000000000000000000000
χ658888-4-4-4-42-42-42-42-400-12-12-12-12000000440000-2-2-2-20000000000-2-2000011110000000000000000000000
χ668888-4-4-4-42-42-42-42-400-12-12-12-12000000-4-4000022220000000000220000-1-1-1-10000000000000000000000
χ678888-4-4-4-4-42-42-42-42002-12-12-12-100004400-2-2-2-2000000000000-2-200111100000000000000000000000000
χ688888-4-4-4-4-42-42-42-42002-12-12-12-10000-4-40022220000000000002200-1-1-1-100000000000000000000000000
χ6988-8-8-4-4442-42-4-24-2400-12-121-21-20000004-40000-2-2220000000000-22000011-1-10000000000000000000000
χ7088-8-8-4-4442-42-4-24-2400-12-121-21-2000000-44000022-2-200000000002-20000-1-1110000000000000000000000
χ7188-8-8-4-444-42-424-24-2002-12-1-21-2100004-400-2-222000000000000-220011-1-100000000000000000000000000
χ7288-8-8-4-444-42-424-24-2002-12-1-21-210000-440022-2-20000000000002-200-1-11100000000000000000000000000
χ738-88-88-88-82-4-242-4-24002-4-242-4-240000000000000000000000000000000000000000000000000000000000
χ748-88-88-88-8-424-2-424-200-424-2-424-20000000000000000000000000000000000000000000000000000000000
χ758-88-8-44-442-4-242-4-2400-121-2-121-2000000000000−2i32i3−2i32i30000000000000000i3−i3i3−i30000000000000000000000
χ768-88-8-44-442-4-242-4-2400-121-2-121-20000000000002i3−2i32i3−2i30000000000000000−i3i3−i3i30000000000000000000000
χ778-88-8-44-44-424-2-424-2002-1-212-1-2100000000−2i32i3−2i32i30000000000000000i3−i3i3−i300000000000000000000000000
χ788-88-8-44-44-424-2-424-2002-1-212-1-21000000002i3−2i32i3−2i30000000000000000−i3i3−i3i300000000000000000000000000
χ798-8-888-8-882-4-24-242-4002-4-24-242-40000000000000000000000000000000000000000000000000000000000
χ808-8-888-8-88-424-24-2-4200-424-24-2-420000000000000000000000000000000000000000000000000000000000
χ818-8-88-444-42-4-24-242-400-121-21-2-12000000000000−2i32i32i3−2i30000000000000000i3−i3−i3i30000000000000000000000
χ828-8-88-444-42-4-24-242-400-121-21-2-120000000000002i3−2i3−2i32i30000000000000000−i3i3i3−i30000000000000000000000
χ838-8-88-444-4-424-24-2-42002-1-21-212-100000000−2i32i32i3−2i30000000000000000i3−i3−i3i300000000000000000000000000
χ848-8-88-444-4-424-24-2-42002-1-21-212-1000000002i3−2i3−2i32i30000000000000000−i3i3i3−i300000000000000000000000000

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