Finite Group Databasebeta

← Group #72310756

Character table — Group #72310756

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11222444444444444444444888888888888888888888816163232323232323232323232323232323232323232323232
order1222222222222224444444422222222222244444444444444444444444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ911111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1211111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1311111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ1411111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ1511111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii
χ1611111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i
χ172222222222222-2-2-2-2-2-222-2-2-2-22-2000000002-20000000022-22-200000000000000000000
χ182222222222222-2-2-2-2-2-222-2-2-2-22-2000000002-200000000-2-22-2200000000000000000000
χ1922222222222-2-222-2-2-2-2-2-222-2-2-2200000000-220000000022-2-2200000000000000000000
χ2022222222222-2-222-2-2-2-2-2-222-2-2-2200000000-2200000000-2-222-200000000000000000000
χ212222222-2-2-2-2222222-2-222-2-22-2-2200000000-2-2000000000000000000000000000002-22-2
χ222222222-2-2-2-2222222-2-222-2-22-2-2200000000-2-200000000000000000000000000000-22-22
χ232222222-2-2-2-222-2-2-2-2222222-22-2-200000000-22000000000000000002-22-2000000000000
χ242222222-2-2-2-222-2-2-2-2222222-22-2-200000000-2200000000000000000-22-22000000000000
χ252222222-2-2-2-2-2-222-2-222-2-2-2-2-2222000000002-2000000000000000002i−2i−2i2i000000000000
χ262222222-2-2-2-2-2-222-2-222-2-2-2-2-2222000000002-200000000000000000−2i2i2i−2i000000000000
χ272222222-2-2-2-2-2-2-2-222-2-2-2-2222-22-20000000022000000000000000000000000000002i−2i−2i2i
χ282222222-2-2-2-2-2-2-2-222-2-2-2-2222-22-2000000002200000000000000000000000000000−2i2i2i−2i
χ2922222-2-222-2-22222-2-222-2-2222-22-200000000-2-200000000000000000000000002-22-20000
χ3022222-2-222-2-22222-2-222-2-2222-22-200000000-2-20000000000000000000000000-22-220000
χ3122222-2-222-2-222-2-222-2-2-2-2-2-2-222200000000-220000000000000000000002i−2i2i−2i00000000
χ3222222-2-222-2-222-2-222-2-2-2-2-2-2-222200000000-22000000000000000000000−2i2i−2i2i00000000
χ3322222-2-222-2-2-2-22222-2-22222-22-2-2000000002-20000000000000000000002-2-2200000000
χ3422222-2-222-2-2-2-22222-2-22222-22-2-2000000002-2000000000000000000000-222-200000000
χ3522222-2-222-2-2-2-2-2-2-2-22222-2-22-2-22000000002200000000000000000000000002i−2i−2i2i0000
χ3622222-2-222-2-2-2-2-2-2-2-22222-2-22-2-2200000000220000000000000000000000000−2i2i2i−2i0000
χ3722222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2000000002200000000000002-22-20000000000000000
χ3822222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-200000000220000000000000-22-220000000000000000
χ3922222-2-2-2-22222-2-22222-2-222-2-2-2222-2-222-2-22-222-2-222-2-20000000000000000000000000
χ4022222-2-2-2-22222-2-22222-2-222-2-2-22-2-222-2-2222-2-2-222-2-2220000000000000000000000000
χ4122222-2-2-2-222-2-222222222-2-2-2-22-222-2-2-2-222-2222-2-2-2-2220000000000000000000000000
χ4222222-2-2-2-222-2-222222222-2-2-2-22-2-2-22222-2-2-22-2-22222-2-20000000000000000000000000
χ4322222-2-2-2-222-2-2-2-2-2-2-2-22222222200000000-2-200000000000002-2-220000000000000000
χ4422222-2-2-2-222-2-2-2-2-2-2-2-22222222200000000-2-20000000000000-222-20000000000000000
χ45444-4-400004-400004-44-4000000000000004400000000-4-40000000000000000000000000
χ46444-4-400004-400004-44-400000000000000-4-400000000440000000000000000000000000
χ47444-4-400004-40000-44-440000000000004400000000-4-4000000000000000000000000000
χ48444-4-400004-40000-44-44000000000000-4-40000000044000000000000000000000000000
χ49444-4-40000-4400004-4-44000000004400000000-4-40000000000000000000000000000000
χ50444-4-40000-4400004-4-4400000000-4-400000000440000000000000000000000000000000
χ51444-4-40000-440000-444-400000000004400000000-4-400000000000000000000000000000
χ52444-4-40000-440000-444-40000000000-4-4000000004400000000000000000000000000000
χ5344-44-4004-400004-40000004-400002-22-22-22-2002-22-22-22-20000000000000000000000000
χ5444-44-4004-400004-40000004-40000-22-22-22-2200-22-22-22-220000000000000000000000000
χ5544-44-4004-40000-44000000-4400002-22-2-22-22002-22-2-22-220000000000000000000000000
χ5644-44-4004-40000-44000000-440000-22-222-22-200-22-222-22-20000000000000000000000000
χ5744-44-400-4400004-4000000-4400002-2-22-222-2002-2-22-222-20000000000000000000000000
χ5844-44-400-4400004-4000000-440000-222-22-2-2200-222-22-2-220000000000000000000000000
χ5944-44-400-440000-440000004-400002-2-222-2-22002-2-222-2-220000000000000000000000000
χ6044-44-400-440000-440000004-40000-222-2-222-200-222-2-222-20000000000000000000000000
χ6144-4-444-400004-40000004-40000002-22-22-22-200-22-22-22-220000000000000000000000000
χ6244-4-444-400004-40000004-4000000-22-22-22-22002-22-22-22-20000000000000000000000000
χ6344-4-444-40000-44000000-440000002-22-2-22-2200-22-222-22-20000000000000000000000000
χ6444-4-444-40000-44000000-44000000-22-222-22-2002-22-2-22-220000000000000000000000000
χ6544-4-44-4400004-4000000-440000002-2-222-2-2200-222-2-222-20000000000000000000000000
χ6644-4-44-4400004-4000000-44000000-222-2-222-2002-2-222-2-220000000000000000000000000
χ6744-4-44-440000-440000004-40000002-2-22-222-200-222-22-2-220000000000000000000000000
χ6844-4-44-440000-440000004-4000000-222-22-2-22002-2-22-222-20000000000000000000000000
χ6916-1600000000000000000000000000000000000000000004i−4i00000000000000000000000
χ7016-160000000000000000000000000000000000000000000−4i4i00000000000000000000000

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