Finite Group Databasebeta

← Group #72213544

Character table — Group #72213544

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122244444444888888888881616161616161616161616163232323232323232323232323232323232323232323264646464646464646464646464646464
order12222222244442222244444422224444444422444444444444444488884444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-11-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111
χ3111111111111111111111111111111111111-11-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1
χ51111111111111111111111111111111-1-1-1-1111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-1-1-111-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111111-1-1-1-1
χ71111111111111111111111111111111-1-1-1-11-11-11-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111111111
χ9111111-11-1111111-1-1-1-1-111-1-111-1-111-1ii−i−i-11111-1-1-1-1i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−iii−i−i
χ10111111-11-1111111-1-1-1-1-111-1-111-1-111-1ii−i−i-11-11-1-1-111i−i-1-111ii−i−i-1-111−i−iii1-11-1−i−iiiii−i−i
χ11111111-11-1111111-1-1-1-1-111-1-111-1-111-1ii−i−i-1-11-1111-1-1i−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i−i−iii
χ12111111-11-1111111-1-1-1-1-111-1-111-1-111-1ii−i−i-1-1-1-1-11111i−i11-1-1ii−i−i-1-111ii−i−i-11-11−i−iii−i−iii
χ13111111-11-1111111-1-1-1-1-111-1-111-1-111-1−i−iii-11111-1-1-1-1−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii−i−iii
χ14111111-11-1111111-1-1-1-1-111-1-111-1-111-1−i−iii-11-11-1-1-111−ii-1-111−i−iii-1-111ii−i−i1-11-1ii−i−i−i−iii
χ15111111-11-1111111-1-1-1-1-111-1-111-1-111-1−i−iii-1-11-1111-1-1−ii-1-111−i−iii11-1-1ii−i−i-1-111−i−iiiii−i−i
χ16111111-11-1111111-1-1-1-1-111-1-111-1-111-1−i−iii-1-1-1-1-11111−ii11-1-1−i−iii-1-111−i−iii-11-11ii−i−iii−i−i
χ172222222222222222-2-222-2-2-2-2-2-22-22-2-20000220202200000000000000000000-200-200000000
χ182222222222222222-2-222-2-2-2-2-2-22-22-2-200002-20-20-2-200000000000000000000200200000000
χ192222222222222-2-222222-2-2-2-222-22-2-2-20000-2000000000022220000000000000-2-2000000000
χ202222222222222-2-222222-2-2-2-222-22-2-2-20000-20000000000-2-2-2-2000000000000022000000000
χ212222222222222-2-22-2-2222222-2-2-2-2-2220000-2020200220000000000-2-2-2-20000000000000000
χ222222222222222-2-22-2-2222222-2-2-2-2-2220000-20-20-200-2-2000000000022220000000000000000
χ23222222-22-2222222-222-2-2-2-222-2-2-222-220000-22020-2-200000000000000000000-200200000000
χ24222222-22-2222222-222-2-2-2-222-2-2-222-220000-2-20-202200000000000000000000200-200000000
χ25222222-22-22222-2-2-222-2-222-2-2-2-222-22-200002020200-2-20000000000-2-2220000000000000000
χ26222222-22-22222-2-2-222-2-222-2-2-2-222-22-2000020-20-20022000000000022-2-20000000000000000
χ27222222-22-22222-2-2-2-2-2-2-2-2-222222-2-2-2200002000000000022-2-20000000000000-22000000000
χ28222222-22-22222-2-2-2-2-2-2-2-2-222222-2-2-22000020000000000-2-22200000000000002-2000000000
χ2922222-22-222-2-2222-2222-222222-22-2-2-2-20000-20000000000000000000000000000002-22-20000
χ3022222-22-222-2-2222-2222-222222-22-2-2-2-20000-2000000000000000000000000000000-22-220000
χ3122222-22-222-2-2222-2-2-22-2-2-2-2-2-2222-2220000-200000000000000000000002i−2i2i−2i000000000000
χ3222222-22-222-2-2222-2-2-22-2-2-2-2-2-2222-2220000-20000000000000000000000−2i2i−2i2i000000000000
χ3322222-22-222-2-22-2-2-2222-2-2-2-2-22-2-2-22220000200000000000000000000000000000000002-22-2
χ3422222-22-222-2-22-2-2-2222-2-2-2-2-22-2-2-2222000020000000000000000000000000000000000-22-22
χ3522222-22-222-2-22-2-2-2-2-22-22222-22-222-2-22222200000000220000-2-2-2-200000000000000000000
χ3622222-22-222-2-22-2-2-2-2-22-22222-22-222-2-2-2-2-2-2200000000-2-20000222200000000000000000000
χ3722222-2-2-2-22-2-2222222-22-2-222-22-2-2-22-20000200000000000000000000002-2-22000000000000
χ3822222-2-2-2-22-2-2222222-22-2-222-22-2-2-22-2000020000000000000000000000-222-2000000000000
χ3922222-2-2-2-22-2-22222-2-2-2222-2-22-2-22-2-22000020000000000000000000000000000002i−2i−2i2i0000
χ4022222-2-2-2-22-2-22222-2-2-2222-2-22-2-22-2-2200002000000000000000000000000000000−2i2i2i−2i0000
χ4122222-2-2-2-22-2-22-2-2222-2222-2-2-222-22-222i2i−2i−2i-2000000002i−2i0000−2i−2i2i2i00000000000000000000
χ4222222-2-2-2-22-2-22-2-2222-2222-2-2-222-22-22−2i−2i2i2i-200000000−2i2i00002i2i−2i−2i00000000000000000000
χ4322222-2-2-2-22-2-22-2-22-2-2-22-2-2222-22222-20000-200000000000000000000000000000000002i−2i−2i2i
χ4422222-2-2-2-22-2-22-2-22-2-2-22-2-2222-22222-20000-20000000000000000000000000000000000−2i2i2i−2i
χ45444444444-4-4-4-400400-4-4000000000002222000000000-2-200002-22-200000000000000000000
χ46444444444-4-4-4-400400-4-400000000000-2-2-2-2000000000220000-22-2200000000000000000000
χ47444444-44-4-4-4-4-400-40044000000000002i2i−2i−2i000000000−2i2i00002i−2i−2i2i00000000000000000000
χ48444444-44-4-4-4-4-400-4004400000000000−2i−2i2i2i0000000002i−2i0000−2i2i2i−2i00000000000000000000
χ4944444-44-44-444-400-400-44000000000002222000000000-2-20000-22-2200000000000000000000
χ5044444-44-44-444-400-400-4400000000000-2-2-2-20000000002200002-22-200000000000000000000
χ5144444-4-4-4-4-444-4004004-4000000000002i2i−2i−2i000000000−2i2i0000−2i2i2i−2i00000000000000000000
χ5244444-4-4-4-4-444-4004004-400000000000−2i−2i2i2i0000000002i−2i00002i−2i−2i2i00000000000000000000
χ5344-4-440000-40044-404-400004-4000000000000020-2002-200000000002-22-20000000000000000
χ5444-4-440000-40044-404-400004-40000000000000-20200-220000000000-22-220000000000000000
χ5544-4-440000-40044-40-440000-44000000000000020-200-2200000000002-2-220000000000000000
χ5644-4-440000-40044-40-440000-440000000000000-202002-20000000000-222-20000000000000000
χ5744-4-440000-4004-4404-40000-44000000000000020-200-220000000000-222-20000000000000000
χ5844-4-440000-4004-4404-40000-440000000000000-202002-200000000002-2-220000000000000000
χ5944-4-440000-4004-440-4400004-4000000000000020-2002-20000000000-22-220000000000000000
χ6044-4-440000-4004-440-4400004-40000000000000-20200-2200000000002-22-20000000000000000
χ61888-8-880-800000000000000000000000000000000000000004i−4i000000000000000000000000
χ62888-8-880-80000000000000000000000000000000000000000−4i4i000000000000000000000000
χ63888-8-8-808000000000000000000000000000000000000004-400000000000000000000000000
χ64888-8-8-80800000000000000000000000000000000000000-4400000000000000000000000000
χ6588-88-8000008-800000000000000000000000000004-400000000000000000000000000000000
χ6688-88-8000008-80000000000000000000000000000-4400000000000000000000000000000000
χ6788-88-800000-8800000000000000000000000040-400000000000000000000000000000000000
χ6888-88-800000-88000000000000000000000000-40400000000000000000000000000000000000
χ6988-8-880000800-800000008-80000000000000000000000000000000000000000000000000000
χ7088-8-880000800-80000000-880000000000000000000000000000000000000000000000000000
χ7116-16000080-800000000000000000000004i−4i4i−4i000000000000000000000000000000000000000
χ7216-16000080-80000000000000000000000−4i4i−4i4i000000000000000000000000000000000000000
χ7316-160000-80800000000000000000000004-4-44000000000000000000000000000000000000000
χ7416-160000-8080000000000000000000000-444-4000000000000000000000000000000000000000

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