Finite Group Databasebeta

← Group #72252407

Character table — Group #72252407

Order 12288.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size112488121216161616161616242424243248484848484848484848646464649696128128128128128128128128192192192192192192192256256256256256256256256256256256256256256256256384384384384512512512512512512
order12222222222244422444222224444433662444666666444444466666666661212121212124488121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111−1+i32−1−i32−1+i32−1−i321111−1+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+i32−1+i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ3111111111111111111111111111111−1−i32−1+i32−1−i32−1+i321111−1−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−i32−1−i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ41111111111-1-11111111-1111-1-11111111111-1-1-1111111111-1-1-1-1111-1-1111-1-1111111-1-111-1-1-1-1-1-1
χ51111111111-1-11111111-1111-1-111111−1+i32−1−i32−1+i32−1−i321-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111-1-1-1-1−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1111−i321−i321−i321+i321+i321+i32
χ61111111111-1-11111111-1111-1-111111−1−i32−1+i32−1−i32−1+i321-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111-1-1-1-1−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1111+i321+i321+i321−i321−i321−i32
χ711111111-1-1111-1-1111111-1-1111-1-111111111-1-111111111111111-1-1111-1-1111-1-11-1-1-1-1-1-11-1-11-1-1
χ811111111-1-1111-1-1111111-1-1111-1-111−1+i32−1−i32−1+i32−1−i3211-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111−1+i321−i321−i32−1+i32−1+i32−1−i321+i321+i32−1−i32−1−i32−1+i321−i321−i32−1−i321+i321+i32-1-1-1-1−1+i321−i321−i32−1−i321+i321+i32
χ911111111-1-1111-1-1111111-1-1111-1-111−1−i32−1+i32−1−i32−1+i3211-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111−1−i321+i321+i32−1−i32−1−i32−1+i321−i321−i32−1+i32−1+i32−1−i321+i321+i32−1+i321−i321−i32-1-1-1-1−1−i321+i321+i32−1+i321−i321−i32
χ1011111111-1-1-1-11-1-11111-11-1-1-1-11-1-11111111-111111111111-1-1-1-11-1-1-1-11-1-1-1-11-1-11-1-111-1-1-111-111
χ1111111111-1-1-1-11-1-11111-11-1-1-1-11-1-111−1+i32−1−i32−1+i32−1−i321-111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111-1-1-1-1−1+i321−i321−i321−i321−i32−1−i321+i321+i321+i321+i32−1+i321−i321−i32−1−i321+i321+i3211-1-11−i32−1+i32−1+i321+i32−1−i32−1−i32
χ1211111111-1-1-1-11-1-11111-11-1-1-1-11-1-111−1−i32−1+i32−1−i32−1+i321-111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111-1-1-1-1−1−i321+i321+i321+i321+i32−1+i321−i321−i321−i321−i32−1−i321+i321+i32−1+i321−i321−i3211-1-11+i32−1−i32−1−i321−i32−1+i32−1+i32
χ132222-2-2220000-200-2-222020000-20022222220002-2-22-2-22-2-200002000020000-200-2000000000000
χ142222-2-2220000-200-2-222020000-20022−1+i3−1−i3−1+i3−1−i32000−1+i31−i31−i3−1−i31+i31+i32-2-20000−1+i30000−1−i300001−i3001+i3000000000000
χ152222-2-2220000-200-2-222020000-20022−1−i3−1+i3−1−i3−1+i32000−1−i31+i31+i3−1+i31−i31−i32-2-20000−1−i30000−1+i300001+i3001−i3000000000000
χ1633333333333333333333333-1-1333-1-10000-1-133000000-1-1-13-1-1-10000000000000000-1-1-1-1000000
χ173333333333-3-33333333-333311333-1-10000-11-3-3000000-1-1-1-3111000000000000000011-1-1000000
χ1833333333-3-3333-3-3333333-3-3-1-13-3-3-1-10000-1-1-3-3000000-1-1-13-1-1-100000000000000001111000000
χ1933333333-3-3-3-33-3-33333-33-3-3113-3-3-1-10000-1133000000-1-1-1-31110000000000000000-1-111000000
χ20444-4444-42-244-42-20000-402-20002-2001111002-21111110000000-11-111-11-111-11-1-11-10000-11-1-11-1
χ21444-4444-42-244-42-20000-402-20002-200−1+i32−1−i32−1+i32−1−i32002-2−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000001−i32−1+i321−i32−1+i32−1+i321+i32−1−i321+i32−1−i32−1−i321−i32−1+i321−i321+i32−1−i321+i3200001−i32−1+i321−i321+i32−1−i321+i32
χ22444-4444-42-244-42-20000-402-20002-200−1−i32−1+i32−1−i32−1+i32002-2−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000001+i32−1−i321+i32−1−i32−1−i321−i32−1+i321−i32−1+i32−1+i321+i32−1−i321+i321−i32−1+i321−i3200001+i32−1−i321+i321−i32−1+i321−i32
χ23444-4444-42-2-4-4-42-20000402-20002-200111100-221111110000000-11-1-1-1-11-1-1-1-11-1-11-100001-111-11
χ24444-4444-42-2-4-4-42-20000402-20002-200−1+i32−1−i32−1+i32−1−i3200-22−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000001−i32−1+i321−i321−i321−i321+i32−1−i321+i321+i321+i321−i32−1+i321−i321+i32−1−i321+i320000−1+i321−i32−1+i32−1−i321+i32−1−i32
χ25444-4444-42-2-4-4-42-20000402-20002-200−1−i32−1+i32−1−i32−1+i3200-22−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000001+i32−1−i321+i321+i321+i321−i32−1+i321−i321−i321−i321+i32−1−i321+i321−i32−1+i321−i320000−1−i321+i32−1−i32−1+i321−i32−1+i32
χ26444-4444-4-2244-4-220000-40-22000-2200111100-221111110000000-1-1111-1-1111-1-11-1-110000-1-11-1-11
χ27444-4444-4-2244-4-220000-40-22000-2200−1+i32−1−i32−1+i32−1−i3200-22−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000001−i321−i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1−i321−i321−i32−1+i321+i321+i32−1−i3200001−i321−i32−1+i321+i321+i32−1−i32
χ28444-4444-4-2244-4-220000-40-22000-2200−1−i32−1+i32−1−i32−1+i3200-22−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000001+i321+i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1+i321+i321+i32−1−i321−i321−i32−1+i3200001+i321+i32−1−i321−i321−i32−1+i32
χ29444-4444-4-22-4-4-4-22000040-22000-22001111002-21111110000000-1-11-1-1-1-11-1-1-1-11-1-11000011-111-1
χ30444-4444-4-22-4-4-4-22000040-22000-2200−1+i32−1−i32−1+i32−1−i32002-2−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000001−i321−i32−1+i321−i321−i321+i321+i32−1−i321+i321+i321−i321−i32−1+i321+i321+i32−1−i320000−1+i32−1+i321−i32−1−i32−1−i321+i32
χ31444-4444-4-22-4-4-4-22000040-22000-2200−1−i32−1+i32−1−i32−1+i32002-2−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000001+i321+i32−1−i321+i321+i321−i321−i32−1+i321−i321−i321+i321+i32−1−i321−i321−i32−1+i320000−1−i32−1−i321+i32−1+i32−1+i321−i32
χ32666666660066600-2-2-2-26-20022-2002200002200000000-22-2-22-2-200000000000000000000000000
χ33666666660066600-2-2-2-26-200-2-2-200-2-20000-2-2000000002-22-2-22200000000000000000000000000
χ346666666600-6-6600-2-2-2-2-6-20022-200-2-20000-22000000002-2222-2-200000000000000000000000000
χ356666666600-6-6600-2-2-2-2-6-200-2-2-2002200002-200000000-22-22-22200000000000000000000000000
χ366666-6-6660000-60022-2-20-20000200-2-20000-200000000022-2004-400000000000000000000000000
χ376666-6-6660000-60022-2-20-20000200-2-20000-200000000022-200-4400000000000000000000000000
χ386666-6-6660000-60022-2-20-200442002200002400000000-2-220-40000000000000000000000000000
χ396666-6-6660000-60022-2-20-200-4-42002200002-400000000-2-22040000000000000000000000000000
χ406666-6-6660000-600-6-666060000-600-2-20000-2000000000-222000000000000000000000000000000
χ41888-8-8-88-80000800000000000000000222200002-2-22-2-20000000-20000-200002002000000000000
χ42888-8-8-88-80000800000000000000000−1+i3−1−i3−1+i3−1−i30000−1+i31−i31−i3−1−i31+i31+i300000001−i300001+i30000−1+i300−1−i3000000000000
χ43888-8-8-88-80000800000000000000000−1−i3−1+i3−1−i3−1+i30000−1−i31+i31+i3−1+i31−i31−i300000001+i300001−i30000−1−i300−1+i3000000000000
χ4488-804-4002-6000-264-44-40022000-2-20022220000-22-2-22-20000000002000020000-200-20000000000
χ4588-804-4002-6000-264-44-40022000-2-200−1+i3−1−i3−1+i3−1−i300001−i3−1+i31−i31+i3−1−i31+i3000000000−1+i30000−1−i300001−i3001+i30000000000
χ4688-804-4002-6000-264-44-40022000-2-200−1−i3−1+i3−1−i3−1+i300001+i3−1−i31+i31−i3−1+i31−i3000000000−1−i30000−1+i300001+i3001−i30000000000
χ4788-804-400-260002-64-44-400-2-2000220022220000-22-2-22-2000000000-20000-2000020020000000000
χ4888-804-400-260002-64-44-400-2-20002200−1+i3−1−i3−1+i3−1−i300001−i3−1+i31−i31+i3−1−i31+i30000000001−i300001+i30000−1+i300−1−i30000000000
χ4988-804-400-260002-64-44-400-2-20002200−1−i3−1+i3−1−i3−1+i300001+i3−1−i31+i31−i3−1+i31−i30000000001+i300001−i30000−1−i300−1+i30000000000
χ5088-80-44006-2000-62-444-400-2-2000220022220000-2-22-2-2200000000-20000-20000200200000000000
χ5188-80-44006-2000-62-444-400-2-20002200−1+i3−1−i3−1+i3−1−i300001−i31−i3−1+i31+i31+i3−1−i3000000001−i300001+i30000−1+i300−1−i300000000000
χ5288-80-44006-2000-62-444-400-2-20002200−1−i3−1+i3−1−i3−1+i300001+i31+i3−1−i31−i31−i3−1+i3000000001+i300001−i30000−1−i300−1+i300000000000
χ5388-80-4400-620006-2-444-40022000-2-20022220000-2-22-2-22000000002000020000-200-200000000000
χ5488-80-4400-620006-2-444-40022000-2-200−1+i3−1−i3−1+i3−1−i300001−i31−i3−1+i31+i31+i3−1−i300000000−1+i30000−1−i300001−i3001+i300000000000
χ5588-80-4400-620006-2-444-40022000-2-200−1−i3−1+i3−1−i3−1+i300001+i31+i3−1−i31−i31−i3−1+i300000000−1−i30000−1+i300001+i3001−i300000000000
χ561212121200-4-4660006600440-4-2-2000-2-2440000-40000000000000000000000000000000000-22000000
χ571212121200-4-4660006600440-4-2-2000-2-2-4-40000400000000000000000000000000000000002-2000000
χ581212121200-4-4-6-6000-6-600440-42200022440000-400000000000000000000000000000000002-2000000
χ591212121200-4-4-6-6000-6-600440-42200022-4-4000040000000000000000000000000000000000-22000000
χ60121212-1200-446-60006-6440000-2244-4-220000000-40000000000000000000000000000000-2200000000
χ61121212-1200-446-60006-6440000-22-4-4-4-220000000400000000000000000000000000000002-200000000
χ62121212-1200-44-66000-664400002-244-42-20000000-400000000000000000000000000000002-200000000
χ63121212-1200-44-66000-664400002-2-4-4-42-2000000040000000000000000000000000000000-2200000000
χ6416-16000000004-4000000000004-40004-444-4-4000000000000000000002-20002-20000000000000000
χ6516-16000000004-4000000000004-40004-4−2+2i3−2−2i32−2i32+2i300000000000000000000−1+i31−i3000−1−i31+i30000000000000000
χ6616-16000000004-4000000000004-40004-4−2−2i3−2+2i32+2i32−2i300000000000000000000−1−i31+i3000−1+i31−i30000000000000000
χ6716-1600000000-4400000000000-440004-444-4-400000000000000000000-22000-220000000000000000
χ6816-1600000000-4400000000000-440004-4−2+2i3−2−2i32−2i32+2i3000000000000000000001−i3−1+i30001+i3−1−i30000000000000000
χ6916-1600000000-4400000000000-440004-4−2−2i3−2+2i32+2i32−2i3000000000000000000001+i3−1−i30001−i3−1+i30000000000000000
χ702424242400-8-8000000000-8-80800000000000000000000000000000000000000000000000000000000
χ71242424-2400-880000000-8-8000000008000000000000000000000000000000000000000000000000000
χ722424-24012-120066000-6-6-44-44006-2000-620000000000000000000000000000000000000000000000000
χ732424-24012-1200-6-600066-44-4400-620006-20000000000000000000000000000000000000000000000000
χ742424-240-12120066000-6-64-4-4400-260002-60000000000000000000000000000000000000000000000000
χ752424-240-121200-6-6000664-4-44002-6000-260000000000000000000000000000000000000000000000000
χ7648-480000000012-1200000000000-44000-4400000000000000000000000000000000000000000000000
χ7748-4800000000-1212000000000004-4000-4400000000000000000000000000000000000000000000000

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