Finite Group Databasebeta

← Group #72231656

Character table — Group #72231656

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222444444444444444888888888888816161616161616161616161616161616161616161616161616323232323232484848484848484896969696
order12222362222224466666662246666661212121222444444666661212121212121212121212124412121212244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-11-111-1-1111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111-11-111-1-1111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111111111111111111-11-11-1-1111-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111
χ611111111111111111111111111111111111-11-11-1-1111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ92222222222-2-22-2-222222222-2-222-2-2-2-2-2-2-2-200000000200000000000000002-222-2-2000000000000
χ102222222222-2-22-2-222222222-2-222-2-2-2-2-2-2-2-20000000020000000000000000-22-2-222000000000000
χ1122222222-2-2222-2-22-2-2-2-222-22-2222222-2-2-2-200000000-20000000000000000000000000000002-200
χ1222222222-2-2222-2-22-2-2-2-222-22-2222222-2-2-2-200000000-2000000000000000000000000000000-2200
χ1322222222-2-2-2-22222-2-2-2-222-2-2222-2-2-2-2222200000000-2000000000000000000000000000000002-2
χ1422222222-2-2-2-22222-2-2-2-222-2-2222-2-2-2-2222200000000-200000000000000000000000000000000-22
χ152222222-22222-2-2-22222222-2-22-2-222-2-222-2-22020-2-200-222002200-2-2-2-20000000000000000000000
χ162222222-22222-2-2-22222222-2-22-2-222-2-222-2-2-20-202200-2-2-200-2-20022220000000000000000000000
χ172222222-222-2-2-2222222222-22-2-2-2-2-222-2-222020200-2-2-2002200220000-2-2-2-2000000000000000000
χ182222222-222-2-2-2222222222-22-2-2-2-2-222-2-2220-20-20022-200-2-200-2-200002222000000000000000000
χ192222222-2-2-222-2222-2-2-2-2222-2-2-2-222-2-2-2-222000000002000000000000000000000022-2-200000000
χ202222222-2-2-222-2222-2-2-2-2222-2-2-2-222-2-2-2-2220000000020000000000000000000000-2-22200000000
χ212222222-2-2-2-2-2-2-2-22-2-2-2-222222-2-2-2-22222-2-2000000002000000000000000000000000002i2i−2i−2i0000
χ222222222-2-2-2-2-2-2-2-22-2-2-2-222222-2-2-2-22222-2-200000000200000000000000000000000000−2i−2i2i2i0000
χ2322222-1-122222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ2422222-1-122222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-12-22-222-2-2-1-1-111-1-111-1-1-1-11111-2-21111000000000000
χ2522222-1-122222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-22-22-2-222-111-1-111-1-11111-1-1-1-1-2-21111000000000000
χ2622222-1-122222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1111111111111111122-1-1-1-1000000000000
χ2722222-1-1222-2-22-2-2-1-1-1-1-1-1-12-2-2-1-11111111100000000-1−i3i3−i3i3−i3i3−i3i3−i3−i3i3i3−i3−i3i3i32-2-1-111000000000000
χ2822222-1-1222-2-22-2-2-1-1-1-1-1-1-12-2-2-1-11111111100000000-1−i3i3i3−i3−i3i3i3−i3−i3−i3i3i3i3i3−i3−i3-2211-1-1000000000000
χ2922222-1-1222-2-22-2-2-1-1-1-1-1-1-12-2-2-1-11111111100000000-1i3−i3−i3i3i3−i3−i3i3i3i3−i3−i3−i3−i3i3i3-2211-1-1000000000000
χ3022222-1-1222-2-22-2-2-1-1-1-1-1-1-12-2-2-1-11111111100000000-1i3−i3i3−i3i3−i3i3−i3i3i3−i3−i3i3i3−i3−i32-2-1-111000000000000
χ3122222-1-1-22222-2-2-2-1-1-1-1-1-1-1-2-2211-1-111-1-1112020-2-2001-1-1−i3i3-1-1−i3i31111i3i3−i3−i300−i3i3−i3i3000000000000
χ3222222-1-1-22222-2-2-2-1-1-1-1-1-1-1-2-2211-1-111-1-1112020-2-2001-1-1i3−i3-1-1i3−i31111−i3−i3i3i300i3−i3i3−i3000000000000
χ3322222-1-1-22222-2-2-2-1-1-1-1-1-1-1-2-2211-1-111-1-111-20-202200111−i3i311−i3i3-1-1-1-1i3i3−i3−i300i3−i3i3−i3000000000000
χ3422222-1-1-22222-2-2-2-1-1-1-1-1-1-1-2-2211-1-111-1-111-20-202200111i3−i311i3−i3-1-1-1-1−i3−i3i3i300−i3i3−i3i3000000000000
χ3522222-1-1-222-2-2-222-1-1-1-1-1-1-1-22-21111-1-111-1-1020200-2-21−i3i3-1-1−i3i3-1-1i3i3−i3−i3111100−i3i3i3−i3000000000000
χ3622222-1-1-222-2-2-222-1-1-1-1-1-1-1-22-21111-1-111-1-1020200-2-21i3−i3-1-1i3−i3-1-1−i3−i3i3i3111100i3−i3−i3i3000000000000
χ3722222-1-1-222-2-2-222-1-1-1-1-1-1-1-22-21111-1-111-1-10-20-200221−i3i311−i3i311i3i3−i3−i3-1-1-1-100i3−i3−i3i3000000000000
χ3822222-1-1-222-2-2-222-1-1-1-1-1-1-1-22-21111-1-111-1-10-20-200221i3−i311i3−i311−i3−i3i3i3-1-1-1-100−i3i3i3−i3000000000000
χ3944444-2-24-4-4444-4-4-22222-2-2-44-4-2-2-2-2-2-222220000000020000000000000000000000000000000000
χ4044444-2-24-4-4-4-4444-22222-2-2-4-44-2-22222-2-2-2-20000000020000000000000000000000000000000000
χ4144444-2-2-4-4-444-444-22222-2-24-4-422-2-22222-2-200000000-20000000000000000000000000000000000
χ4244444-2-2-4-4-4-4-4-4-4-4-22222-2-24442222-2-2-2-22200000000-20000000000000000000000000000000000
χ43444-4-4440000004-4-400004-4000000000004-420-202-20002200-2-2002-22-20000000000000000000000
χ44444-4-4440000004-4-400004-4000000000004-4-2020-22000-2-2002200-22-220000000000000000000000
χ45444-4-444000000-44-400004-400000000000-4420-20-220002200-2-200-22-220000000000000000000000
χ46444-4-444000000-44-400004-400000000000-44-20202-2000-2-20022002-22-20000000000000000000000
χ47444-4-4-2-20000004-42−2i3−2i32i32i3-220000000−2i32i300-2220-202-2000−1−i3−1+i3001+i31−i300−1+i31−i3−1−i31+i30000000000000000000000
χ48444-4-4-2-20000004-42−2i3−2i32i32i3-220000000−2i32i300-22-2020-220001+i31−i300−1−i3−1+i3001−i3−1+i31+i3−1−i30000000000000000000000
χ49444-4-4-2-20000004-422i32i3−2i3−2i3-2200000002i3−2i300-2220-202-2000−1+i3−1−i3001−i31+i300−1−i31+i3−1+i31−i30000000000000000000000
χ50444-4-4-2-20000004-422i32i3−2i3−2i3-2200000002i3−2i300-22-2020-220001−i31+i300−1+i3−1−i3001+i3−1−i31−i3−1+i30000000000000000000000
χ51444-4-4-2-2000000-442−2i3−2i32i32i3-2200000002i3−2i3002-220-20-22000−1−i3−1+i3001+i31−i3001−i3−1+i31+i3−1−i30000000000000000000000
χ52444-4-4-2-2000000-442−2i3−2i32i32i3-2200000002i3−2i3002-2-20202-20001+i31−i300−1−i3−1+i300−1+i31−i3−1−i31+i30000000000000000000000
χ53444-4-4-2-2000000-4422i32i3−2i3−2i3-220000000−2i32i3002-220-20-22000−1+i3−1−i3001−i31+i3001+i3−1−i31−i3−1+i30000000000000000000000
χ54444-4-4-2-2000000-4422i32i3−2i3−2i3-220000000−2i32i3002-2-20202-20001−i31+i300−1+i3−1−i300−1−i31+i3−1+i31−i30000000000000000000000
χ5544-44-4440004-4000-40000-44000004-4000000020-2002-20002200-2-200002-22-2000000000000000000
χ5644-44-4440004-4000-40000-44000004-40000000-20200-22000-2-200220000-22-22000000000000000000
χ5744-44-444000-44000-40000-4400000-44000000020-200-220002200-2-20000-22-22000000000000000000
χ5844-44-444000-44000-40000-4400000-440000000-202002-2000-2-2002200002-22-2000000000000000000
χ5944-44-4-2-20004-40002−2i32i3−2i32i32-200000-2200−2i32i300020-2002-2000−1−i3−1+i3001+i31−i30000−1+i31−i3−1−i31+i3000000000000000000
χ6044-44-4-2-20004-40002−2i32i3−2i32i32-200000-2200−2i32i3000-20200-220001+i31−i300−1−i3−1+i300001−i3−1+i31+i3−1−i3000000000000000000
χ6144-44-4-2-20004-400022i3−2i32i3−2i32-200000-22002i3−2i300020-2002-2000−1+i3−1−i3001−i31+i30000−1−i31+i3−1+i31−i3000000000000000000
χ6244-44-4-2-20004-400022i3−2i32i3−2i32-200000-22002i3−2i3000-20200-220001−i31+i300−1+i3−1−i300001+i3−1−i31−i3−1+i3000000000000000000
χ6344-44-4-2-2000-440002−2i32i3−2i32i32-2000002-2002i3−2i300020-200-22000−1−i3−1+i3001+i31−i300001−i3−1+i31+i3−1−i3000000000000000000
χ6444-44-4-2-2000-440002−2i32i3−2i32i32-2000002-2002i3−2i3000-202002-20001+i31−i300−1−i3−1+i30000−1+i31−i3−1−i31+i3000000000000000000
χ6544-44-4-2-2000-4400022i3−2i32i3−2i32-2000002-200−2i32i300020-200-22000−1+i3−1−i3001−i31+i300001+i3−1−i31−i3−1+i3000000000000000000
χ6644-44-4-2-2000-4400022i3−2i32i3−2i32-2000002-200−2i32i3000-202002-20001−i31+i300−1+i3−1−i30000−1−i31+i3−1+i31−i3000000000000000000
χ6744-4-444404-40000044-4-44-4-4000000000000000000000000000000000000000000002-22-200000000
χ6844-4-444404-40000044-4-44-4-400000000000000000000000000000000000000000000-22-2200000000
χ6944-4-44440-44000004-444-4-4-4000000000000000000000000000000000000000000002-2-2200000000
χ7044-4-44440-44000004-444-4-4-400000000000000000000000000000000000000000000-222-200000000
χ7188-8-88-4-408-800000-4-444-44400000000000000000000000000000000000000000000000000000000
χ7288-8-88-4-40-8800000-44-4-444400000000000000000000000000000000000000000000000000000000
χ738-80008-840000-40000000000004-400000000000000000000000000000000000000000002i−2i2i−2i0000
χ748-80008-840000-40000000000004-40000000000000000000000000000000000000000000−2i2i−2i2i0000
χ758-80008-8-400004000000000000-4400000000000000000000000000000000000000000002-2-220000
χ768-80008-8-400004000000000000-440000000000000000000000000000000000000000000-222-20000
χ7716-16000-8880000-8000000000000-44000000000000000000000000000000000000000000000000000
χ7816-16000-88-8000080000000000004-4000000000000000000000000000000000000000000000000000

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