Finite Group Databasebeta

← Group #72231558

Character table — Group #72231558

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11222222244444444444444888888888888888888888881616161616161616323232323232323232323232484848484848484896969696
order12222366622222222666666222224466666666666666664412121212121244441212121212121212224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ511111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ611111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-111111-11-111-1-1-1-111
χ811111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-11111-11-11-1-11111-1-1
χ92222222222222-2-2-2-222222200002-2-2-2-2-2-200000000222200-2-200002-20022-2-20000000000000000
χ102222222222222-2-2-2-222222200002-2-2-2-2-2-200000000222200-2-20000-2200-2-2220000000000000000
χ1122222222222-2-222222222222222-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ1222222222222-2-22222222222-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222000000000000000000000000
χ1322222222222-2-2-2-2-2-22222220000-222-2-2-2-200000000-2-2-2-200220000002i−2i00002i2i−2i−2i000000000000
χ1422222222222-2-2-2-2-2-22222220000-222-2-2-2-200000000-2-2-2-20022000000−2i2i0000−2i−2i2i2i000000000000
χ15222222222-2-22222-2-222-2-2-2-20000-22-222-2-20000000022-2-2002-20000000000000000020200-2-20000
χ16222222222-2-22222-2-222-2-2-2-20000-22-222-2-20000000022-2-2002-200000000000000000-20-200220000
χ17222222222-2-222-2-22222-2-2-2-20000-2-22-2-2220000000022-2-200-2200000000000000002020-2-2000000
χ18222222222-2-222-2-22222-2-2-2-20000-2-22-2-2220000000022-2-200-220000000000000000-20-2022000000
χ19222222222-2-2-2-222-2-222-2-2-2-200002-2222-2-200000000-2-22200-22000000000000000000000000002-2
χ20222222222-2-2-2-222-2-222-2-2-2-200002-2222-2-200000000-2-22200-2200000000000000000000000000-22
χ21222222222-2-2-2-2-2-22222-2-2-2-2000022-2-2-22200000000-2-222002-20000000000000000000000002-200
χ22222222222-2-2-2-2-2-22222-2-2-2-2000022-2-2-22200000000-2-222002-2000000000000000000000000-2200
χ2322222-1-1-1-122222222-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ2422222-1-1-1-122222222-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111000000000000
χ2522222-1-1-1-122222222-1-1-1-1-1-1-2-2-2-2222-1-1-1-111111111-1-1-1-1-2-2-1-1111122-2-2-1-1-1-11111000000000000
χ2622222-1-1-1-122222222-1-1-1-1-1-1-2-2-2-2222-1-1-1-111111111-1-1-1-1-2-2-1-11111-2-2221111-1-1-1-1000000000000
χ2722222-1-1-1-12222-2-2-2-2-1-1-1-1-1-100002-2-21111−i3−i3−i3−i3i3i3i3i3-1-1-1-10011−i3−i3i3i32-200-1-111−i3i3−i3i3000000000000
χ2822222-1-1-1-12222-2-2-2-2-1-1-1-1-1-100002-2-21111−i3−i3−i3−i3i3i3i3i3-1-1-1-10011−i3−i3i3i3-220011-1-1i3−i3i3−i3000000000000
χ2922222-1-1-1-12222-2-2-2-2-1-1-1-1-1-100002-2-21111i3i3i3i3−i3−i3−i3−i3-1-1-1-10011i3i3−i3−i32-200-1-111i3−i3i3−i3000000000000
χ3022222-1-1-1-12222-2-2-2-2-1-1-1-1-1-100002-2-21111i3i3i3i3−i3−i3−i3−i3-1-1-1-10011i3i3−i3−i3-220011-1-1−i3i3−i3i3000000000000
χ3122222-1-1-1-122-2-22222-1-1-1-1-1-12222-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111-2-211111100003−33−33−3−33000000000000
χ3222222-1-1-1-122-2-22222-1-1-1-1-1-12222-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111-2-21111110000−33−33−333−3000000000000
χ3322222-1-1-1-122-2-22222-1-1-1-1-1-1-2-2-2-2-2-2-2-1-1-1-11111111111112211-1-1-1-100003−33−3−333−3000000000000
χ3422222-1-1-1-122-2-22222-1-1-1-1-1-1-2-2-2-2-2-2-2-1-1-1-11111111111112211-1-1-1-10000−33−333−3−33000000000000
χ3522222-1-1-1-122-2-2-2-2-2-2-1-1-1-1-1-10000-2221111−i3−i3−i3−i3i3i3i3i3111100-1-1i3i3−i3−i3002i−2i3−3−33−i−iii000000000000
χ3622222-1-1-1-122-2-2-2-2-2-2-1-1-1-1-1-10000-2221111−i3−i3−i3−i3i3i3i3i3111100-1-1i3i3−i3−i300−2i2i−333−3ii−i−i000000000000
χ3722222-1-1-1-122-2-2-2-2-2-2-1-1-1-1-1-10000-2221111i3i3i3i3−i3−i3−i3−i3111100-1-1−i3−i3i3i3002i−2i−333−3−i−iii000000000000
χ3822222-1-1-1-122-2-2-2-2-2-2-1-1-1-1-1-10000-2221111i3i3i3i3−i3−i3−i3−i3111100-1-1−i3−i3i3i300−2i2i3−3−33ii−i−i000000000000
χ3944444-2-2-2-2-4-44444-4-4-2-222220000-44-4-2-22200000000-2-22200-220000000000000000000000000000
χ4044444-2-2-2-2-4-444-4-444-2-222220000-4-4422-2-200000000-2-222002-20000000000000000000000000000
χ4144444-2-2-2-2-4-4-4-444-4-4-2-2222200004-44-2-2220000000022-2-2002-20000000000000000000000000000
χ4244444-2-2-2-2-4-4-4-4-4-444-2-22222000044-422-2-20000000022-2-200-220000000000000000000000000000
χ43444-4-44444004-40000-4-4000022-2-2000000022-2-222-2-24-4002-2002-22-2000000000000000000000000
χ44444-4-44444004-40000-4-40000-2-2220000000-2-222-2-2224-400-2200-22-22000000000000000000000000
χ45444-4-4444400-440000-4-4000022-2-2000000022-2-222-2-2-4400-2200-22-22000000000000000000000000
χ46444-4-4444400-440000-4-40000-2-2220000000-2-222-2-222-44002-2002-22-2000000000000000000000000
χ47444-4-4-2-2-2-2004-4000022−2i3−2i32i32i322-2-20000000−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i3-22−2i32i32-200−1−i31+i3−1+i31−i3000000000000000000000000
χ48444-4-4-2-2-2-2004-4000022−2i3−2i32i32i3-2-22200000001+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i3-22−2i32i3-22001+i3−1−i31−i3−1+i3000000000000000000000000
χ49444-4-4-2-2-2-2004-40000222i32i3−2i3−2i322-2-20000000−1+i3−1+i31−i31−i3−1−i3−1−i31+i31+i3-222i3−2i32-200−1+i31−i3−1−i31+i3000000000000000000000000
χ50444-4-4-2-2-2-2004-40000222i32i3−2i3−2i3-2-22200000001−i31−i3−1+i3−1+i31+i31+i3−1−i3−1−i3-222i3−2i3-22001−i3−1+i31+i3−1−i3000000000000000000000000
χ51444-4-4-2-2-2-200-44000022−2i3−2i32i32i322-2-20000000−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i32-22i3−2i3-22001+i3−1−i31−i3−1+i3000000000000000000000000
χ52444-4-4-2-2-2-200-44000022−2i3−2i32i32i3-2-22200000001+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i32-22i3−2i32-200−1−i31+i3−1+i31−i3000000000000000000000000
χ53444-4-4-2-2-2-200-440000222i32i3−2i3−2i322-2-20000000−1+i3−1+i31−i31−i3−1−i3−1−i31+i31+i32-2−2i32i3-22001−i3−1+i31+i3−1−i3000000000000000000000000
χ54444-4-4-2-2-2-200-440000222i32i3−2i3−2i3-2-22200000001−i31−i3−1+i3−1+i31+i31+i3−1−i3−1−i32-2−2i32i32-200−1+i31−i3−1−i31+i3000000000000000000000000
χ5544-44-444-4-40000004-44-400000000000004-400000000000000000000000000000000020-2002-20000
χ5644-44-444-4-40000004-44-400000000000004-4000000000000000000000000000000000-20200-220000
χ5744-44-444-4-4000000-444-40000000000000-4400000000000000000000000000000000020-200-220000
χ5844-44-444-4-4000000-444-40000000000000-44000000000000000000000000000000000-202002-20000
χ5944-4-4444-4-400004-400-44000000000004-4000000000000000000000000000000000020-202-2000000
χ6044-4-4444-4-400004-400-44000000000004-40000000000000000000000000000000000-2020-22000000
χ6144-4-4444-4-40000-4400-4400000000000-44000000000000000000000000000000000020-20-22000000
χ6244-4-4444-4-40000-4400-4400000000000-440000000000000000000000000000000000-20202-2000000
χ6388-88-8-4-4440000008-8-440000000000000-4400000000000000000000000000000000000000000000
χ6488-88-8-4-444000000-88-4400000000000004-400000000000000000000000000000000000000000000
χ6588-8-88-4-44400008-8004-400000000000-440000000000000000000000000000000000000000000000
χ6688-8-88-4-4440000-88004-4000000000004-40000000000000000000000000000000000000000000000
χ678-80008-8004-4000000004-44-4004-40000000004-4004-4000000000000000000000000000000000000
χ688-80008-8004-4000000004-44-400-44000000000-4400-44000000000000000000000000000000000000
χ698-80008-800-4400000000-44-444-40000000004-4004-400000000000000000000000000000000000000
χ708-80008-800-4400000000-44-44-44000000000-4400-4400000000000000000000000000000000000000
χ718-8000-44−4i34i34-400000000−2−2i32+2i3−2+2i32−2i3004-4000000000−2−2i32+2i300−2+2i32−2i3000000000000000000000000000000000000
χ728-8000-44−4i34i34-400000000−2−2i32+2i3−2+2i32−2i300-440000000002+2i3−2−2i3002−2i3−2+2i3000000000000000000000000000000000000
χ738-8000-44−4i34i3-44000000002+2i3−2−2i32−2i3−2+2i34-4000000000−2−2i32+2i300−2+2i32−2i300000000000000000000000000000000000000
χ748-8000-44−4i34i3-44000000002+2i3−2−2i32−2i3−2+2i3-440000000002+2i3−2−2i3002−2i3−2+2i300000000000000000000000000000000000000
χ758-8000-444i3−4i34-400000000−2+2i32−2i3−2−2i32+2i3004-4000000000−2+2i32−2i300−2−2i32+2i3000000000000000000000000000000000000
χ768-8000-444i3−4i34-400000000−2+2i32−2i3−2−2i32+2i300-440000000002−2i3−2+2i3002+2i3−2−2i3000000000000000000000000000000000000
χ778-8000-444i3−4i3-44000000002−2i3−2+2i32+2i3−2−2i34-4000000000−2+2i32−2i300−2−2i32+2i300000000000000000000000000000000000000
χ788-8000-444i3−4i3-44000000002−2i3−2+2i32+2i3−2−2i3-440000000002−2i3−2+2i3002+2i3−2−2i300000000000000000000000000000000000000

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