Finite Group Databasebeta

← Group #72339669

Character table — Group #72339669

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11222222244444488888888888888816161616161616161616161616163232323232323232323232323232323232323232
order1222244442244442222224444444442222444444888844444488888888888888
χ11111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ7111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1111-111-111-111-1-1-1-111-1-1-1-111111111-1-1ii−i−i-1-1ii−i−iii−i−iii−i−i
χ10111111111111-1-1111-111-111-111-1-1-1-111-1-1-1-111111111-1-1−i−iii-1-1−i−iii−i−iii−i−iii
χ11111111111111-1-1111-111-111-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i11ii−i−i−i−iii−i−iii
χ12111111111111-1-1111-111-111-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111−i−iii11−i−iiiii−i−iii−i−i
χ13111111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-111ii−i−i-1-1−i−iiiii−i−i−i−iii
χ14111111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-111−i−iii-1-1ii−i−i−i−iiiii−i−i
χ15111111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1ii−i−i11−i−iii−i−iiiii−i−i
χ16111111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−iii11ii−i−iii−i−i−i−iii
χ17222222222222222-2-2-222-2-2-2-2222-222-2-2-2-2220000000000000000000000000000
χ18222222222222222-2-2-2-2-2-2-2-2-2-2-22-2222222-2-20000000000000000000000000000
χ19222222222222-2-22-2-22222-2-2222-22-2-2-2-222-2-20000000000000000000000000000
χ20222222222222-2-22-2-22-2-22-2-22-2-2-22-2-222-2-2220000000000000000000000000000
χ2122222-2-2-2-2-2-22222222002-2-2-2002-2-2-20000000000000000000000000000002i−2i2i−2i
χ2222222-2-2-2-2-2-22222222002-2-2-2002-2-2-2000000000000000000000000000000−2i2i−2i2i
χ2322222-2-2-2-2-2-22222-2-2-200-22220022-2-2000000000000000000000000002i−2i2i−2i0000
χ2422222-2-2-2-2-2-22222-2-2-200-22220022-2-200000000000000000000000000−2i2i−2i2i0000
χ2522222-2-2-2-2-2-22-2-2222-200-2-2-2200-22220000000000000000000000000000002-2-22
χ2622222-2-2-2-2-2-22-2-2222-200-2-2-2200-2222000000000000000000000000000000-222-2
χ2722222-2-2-2-2-2-22-2-22-2-2200222-200-2-222000000000000000000000000002-2-220000
χ2822222-2-2-2-2-2-22-2-22-2-2200222-200-2-22200000000000000000000000000-222-20000
χ2922-22-222-2-22-2222-22-2200-22-2-200-222-200000000002i2i−2i−2i2i−2i000000000000000000
χ3022-22-222-2-22-2222-22-2200-22-2-200-222-20000000000−2i−2i2i2i−2i2i000000000000000000
χ3122-22-222-2-22-2222-2-22-2002-22200-2-22-20000002i2i−2i−2i00000000002i−2i000000000000
χ3222-22-222-2-22-2222-2-22-2002-22200-2-22-2000000−2i−2i2i2i0000000000−2i2i000000000000
χ3322-22-222-2-22-22-2-2-22-2-20022-22002-2-2200000000002i2i−2i−2i−2i2i000000000000000000
χ3422-22-222-2-22-22-2-2-22-2-20022-22002-2-220000000000−2i−2i2i2i2i−2i000000000000000000
χ3522-22-222-2-22-22-2-2-2-22200-2-22-20022-220000002i2i−2i−2i0000000000−2i2i000000000000
χ3622-22-222-2-22-22-2-2-2-22200-2-22-20022-22000000−2i−2i2i2i00000000002i−2i000000000000
χ3722-22-2-2-222-22222-22-2200-2-22200-2-2-2200000000000000002i−2i2i−2i00000000000000
χ3822-22-2-2-222-22222-22-2200-2-22200-2-2-220000000000000000−2i2i−2i2i00000000000000
χ3922-22-2-2-222-22222-2-22-20022-2-200-22-2200000000000000000000002-22-200000000
χ4022-22-2-2-222-22222-2-22-20022-2-200-22-220000000000000000000000-22-2200000000
χ4122-22-2-2-222-222-2-2-22-2-2002-22-200222-200000000000000002-2-2200000000000000
χ4222-22-2-2-222-222-2-2-22-2-2002-22-200222-20000000000000000-222-200000000000000
χ4322-22-2-2-222-222-2-2-2-22200-22-22002-22-200000000000000000000002i−2i−2i2i00000000
χ4422-22-2-2-222-222-2-2-2-22200-22-22002-22-20000000000000000000000−2i2i2i−2i00000000
χ45444444444-4-4-400-4000440000-4-400000000000000000000000000000000000000
χ46444444444-4-4-400-4000-4-400004400000000000000000000000000000000000000
χ4744444-4-4-4-444-400-400000000000000000004-40000000000000000000000000000
χ4844444-4-4-4-444-400-40000000000000000000-440000000000000000000000000000
χ49444-4-44-44-40000000000000004-400000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ50444-4-44-44-40000000000000004-40000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ51444-4-44-44-4000000000000000-4400000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ52444-4-44-44-4000000000000000-440000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ5344-44-444-4-4-44-40040000000000000004-400000000000000000000000000000000
χ5444-44-444-4-4-44-4004000000000000000-4400000000000000000000000000000000
χ5544-44-4-4-4444-4-4004000000000000000004-4000000000000000000000000000000
χ5644-44-4-4-4444-4-400400000000000000000-44000000000000000000000000000000
χ5744-4-444-4-440000000004-400000000000000002-2-222-2-2200000000000000000000
χ5844-4-444-4-440000000004-40000000000000000-222-2-222-200000000000000000000
χ5944-4-444-4-44000000000-4400000000000000002-2-22-222-200000000000000000000
χ6044-4-444-4-44000000000-440000000000000000-222-22-2-2200000000000000000000
χ61888-8-8-88-880000000000000000000000000000000000000000000000000000000
χ6288-8-88-888-80000000000000000000000000000000000000000000000000000000
χ6316-1600000000008-800000000000000000000000000000000000000000000000000
χ6416-160000000000-8800000000000000000000000000000000000000000000000000

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