Finite Group Databasebeta

← Group #72217355

Character table — Group #72217355

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size112446688888121212121616242424242424484848486464646464646464646496969696969696128128128128128128128128128128128128192192192192256256256256256256256256
order122222222222222224222222224433446666664444444666666666666444466121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ31111111111111111111111111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ41111111111111111-1-11111111-11-111-1-1111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ51111111111111111-1-11111111-11-1−1+i32−1−i32-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211-1-11−i321+i321−i321−i321−i321+i321+i321+i32
χ61111111111111111-1-11111111-11-1−1−i32−1+i32-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211-1-11+i321−i321+i321+i321+i321−i321−i321−i32
χ711111111-1-1-1-111111111-1-1-1-1111111-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-1
χ811111111-1-1-1-111111111-1-1-1-11111−1+i32−1−i32-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32-1-1-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ911111111-1-1-1-111111111-1-1-1-11111−1−i32−1+i32-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32-1-1-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ1011111111-1-1-1-11111-1-111-1-1-1-11-11-11111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-111-111
χ1111111111-1-1-1-11111-1-111-1-1-1-11-11-1−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111-1-1-1-1−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32-1-1111−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32
χ1211111111-1-1-1-11111-1-111-1-1-1-11-11-1−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111-1-1-1-1−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32-1-1111+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32
χ13222-2-222-2000022-2-2002-20000202022002-2-22-2-22-2-200002-200002-20000000000000000
χ14222-2-222-2000022-2-2002-200002020−1+i3−1−i300−1+i31−i31−i3−1−i31+i31+i32-2-20000−1+i31−i30000−1−i31+i30000000000000000
χ15222-2-222-2000022-2-2002-200002020−1−i3−1+i300−1−i31+i31+i3−1+i31−i31−i32-2-20000−1−i31+i30000−1+i31−i30000000000000000
χ16333333333333333333333333-1-1-1-10033000000-1-1-13-1-1-1000000000000-1-1-1-100000000
χ173333333333333333-3-3333333-11-1100-3-3000000-1-1-1-3111000000000000-1-11100000000
χ1833333333-3-3-3-333333333-3-3-3-3-1-1-1-100-3-3000000-1-1-13-1-1-1000000000000111100000000
χ1933333333-3-3-3-33333-3-333-3-3-3-3-11-110033000000-1-1-1-311100000000000011-1-100000000
χ2044-4444-4-422-2-200004-40022-2-20000112-21111110000000-1-111-1-1-1-111-1-1000011-11-1-11-1
χ2144-4444-4-422-2-200004-40022-2-20000−1+i32−1−i322-2−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000001−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i320000−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32
χ2244-4444-4-422-2-200004-40022-2-20000−1−i32−1+i322-2−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000001+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i320000−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32
χ2344-4444-4-422-2-20000-440022-2-2000011-221111110000000-1-111-1-1-1-111-1-10000-1-11-111-11
χ2444-4444-4-422-2-20000-440022-2-20000−1+i32−1−i32-22−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000001−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i3200001−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i32
χ2544-4444-4-422-2-20000-440022-2-20000−1−i32−1+i32-22−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000001+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i3200001+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i32
χ2644-4444-4-4-2-22200004-400-2-222000011-221111110000000-1-1-1-111-1-1-1-111000011-1-11-1-11
χ2744-4444-4-4-2-22200004-400-2-2220000−1+i32−1−i32-22−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000001−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i320000−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32
χ2844-4444-4-4-2-22200004-400-2-2220000−1−i32−1+i32-22−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000001+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i320000−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32
χ2944-4444-4-4-2-2220000-4400-2-2220000112-21111110000000-1-1-1-111-1-1-1-1110000-1-111-111-1
χ3044-4444-4-4-2-2220000-4400-2-2220000−1+i32−1−i322-2−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000001−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i3200001−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32
χ3144-4444-4-4-2-2220000-4400-2-2220000−1−i32−1+i322-2−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000001+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i3200001+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32
χ32666666660000-2-2-2-266-2-2000022220000000000-22-2-22-2-2000000000000000000000000
χ33666666660000-2-2-2-266-2-20000-2-2-2-200000000002-22-2-222000000000000000000000000
χ34666666660000-2-2-2-2-6-6-2-200002-22-20000000000-22-22-222000000000000000000000000
χ35666666660000-2-2-2-2-6-6-2-20000-22-2200000000002-2222-2-2000000000000000000000000
χ36666-6-666-6000066-6-6006-60000-20-200000000000-2220000000000000000000000000000
χ37666-6-666-60000-2-22200-22000024240000000000-2-220-400000000000000000000000000
χ38666-6-666-60000-2-22200-2200002-42-40000000000-2-220400000000000000000000000000
χ39666-6-666-60000-2-22200-220000-20-20000000000022-2004-4000000000000000000000000
χ40666-6-666-60000-2-22200-220000-20-20000000000022-200-44000000000000000000000000
χ4188-8-8-88-880000000000000000000022002-2-22-2-20000000-220000-220000000000000000
χ4288-8-8-88-8800000000000000000000−1+i3−1−i300−1+i31−i31−i3−1−i31+i31+i300000001−i3−1+i300001+i3−1−i30000000000000000
χ4388-8-8-88-8800000000000000000000−1−i3−1+i300−1−i31+i31+i3−1+i31−i31−i300000001+i3−1−i300001−i3−1+i30000000000000000
χ448-804-40002-26-64-44-400002-22-200002200-22-2-22-2000000000002-200002-2000000000000
χ458-804-40002-26-64-44-400002-22-20000−1+i3−1−i3001−i3−1+i31−i31+i3−1−i31+i300000000000−1+i31−i30000−1−i31+i3000000000000
χ468-804-40002-26-64-44-400002-22-20000−1−i3−1+i3001+i3−1−i31+i31−i3−1+i31−i300000000000−1−i31+i30000−1+i31−i3000000000000
χ478-804-4000-22-664-44-40000-22-2200002200-22-2-22-200000000000-220000-22000000000000
χ488-804-4000-22-664-44-40000-22-220000−1+i3−1−i3001−i3−1+i31−i31+i3−1−i31+i3000000000001−i3−1+i300001+i3−1−i3000000000000
χ498-804-4000-22-664-44-40000-22-220000−1−i3−1+i3001+i3−1−i31+i31−i3−1+i31−i3000000000001+i3−1−i300001−i3−1+i3000000000000
χ508-80-440006-62-24-4-440000-22-2200002200-2-22-2-220000000002-200002-200000000000000
χ518-80-440006-62-24-4-440000-22-220000−1+i3−1−i3001−i31−i3−1+i31+i31+i3−1−i3000000000−1+i31−i30000−1−i31+i300000000000000
χ528-80-440006-62-24-4-440000-22-220000−1−i3−1+i3001+i31+i3−1−i31−i31−i3−1+i3000000000−1−i31+i30000−1+i31−i300000000000000
χ538-80-44000-66-224-4-4400002-22-200002200-2-22-2-22000000000-220000-2200000000000000
χ548-80-44000-66-224-4-4400002-22-20000−1+i3−1−i3001−i31−i3−1+i31+i31+i3−1−i30000000001−i3−1+i300001+i3−1−i300000000000000
χ558-80-44000-66-224-4-4400002-22-20000−1−i3−1+i3001+i31+i3−1−i31−i31−i3−1+i30000000001+i3−1−i300001−i3−1+i300000000000000
χ5612121200-4-406666440000-40-2-2-2-240-40000000000000000000000000000002-20000000000
χ5712121200-4-406666440000-40-2-2-2-2-404000000000000000000000000000000-220000000000
χ5812121200-4-40-6-6-6-6440000-40222240-4000000000000000000000000000000-220000000000
χ5912121200-4-40-6-6-6-6440000-402222-4040000000000000000000000000000002-20000000000
χ601212-1200-44066-6-60044000-4-2-222040-40000000000000000000000000000000-2200000000
χ611212-1200-44066-6-60044000-4-2-2220-40400000000000000000000000000000002-200000000
χ621212-1200-440-6-6660044000-422-2-2040-400000000000000000000000000000002-200000000
χ631212-1200-440-6-6660044000-422-2-20-4040000000000000000000000000000000-2200000000
χ6424242400-8-800000-8-80000800000000000000000000000000000000000000000000000000
χ652424-2400-880000000-8-800080000000000000000000000000000000000000000000000000
χ6624-24012-120006-6-66-44-4400006-6-22000000000000000000000000000000000000000000000
χ6724-24012-12000-666-6-44-440000-662-2000000000000000000000000000000000000000000000
χ6824-240-12120006-6-66-444-40000-226-6000000000000000000000000000000000000000000000
χ6924-240-1212000-666-6-444-400002-2-66000000000000000000000000000000000000000000000

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