Finite Group Databasebeta

← Group #72319697

Character table — Group #72319697

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11222444444444444888888888161616161616161616161616161616161616161632323232323232323232323232323232323264646464646464646464646464646464
order12222222244444444222224444222222224444444444442444444444888888884444444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ511111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ611111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ711111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1
χ811111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111
χ911111-1-1111-1-1-1-1111-1-1-111-1-1111-1-111-1-111-11-11111-1-1-1-1111-111-1-1-1-111-1-111-1-11-111-1-111-1-11-111-1-1
χ1011111-1-1111-1-1-1-1111-1-1-111-1-1111-1-111-1-111-11-11111-1-1-1-1-1-11-111-1-11111-1-1-1-111-1111-1-1-1-111-11-1-111
χ1111111-1-1111-1-1-1-1111-1-1-111-1-1111-1-111-1-111-11-1-1-1-1-11111111-111-1-1-1-1-1-11111-1-1-11-1-111-1-111-1111-1-1
χ1211111-1-1111-1-1-1-1111-1-1-111-1-1111-1-111-1-111-11-1-1-1-1-11111-1-11-111-1-111-1-111-1-1111-1-1-11111-1-11-1-1-111
χ1311111-1-1111-1-1-1-1111-1-1-111-1-1111-1-1-1-11111-11-11111-1-1-1-111-11-1-111-1-111-1-111-1-11-1-1-111-1-1111-1-1-111
χ1411111-1-1111-1-1-1-1111-1-1-111-1-1111-1-1-1-11111-11-11111-1-1-1-1-1-1-11-1-1111111-1-1-1-111-11-1-11111-1-1-1111-1-1
χ1511111-1-1111-1-1-1-1111-1-1-111-1-1111-1-1-1-11111-11-1-1-1-1-1111111-11-1-111-1-1-1-11111-1-1-1111-1-111-1-1-11-1-111
χ1611111-1-1111-1-1-1-1111-1-1-111-1-1111-1-1-1-11111-11-1-1-1-1-11111-1-1-11-1-11111-1-111-1-1111-111-1-1-1-1111-111-1-1
χ17222222222222222222-2-2-2-22222-2-2-20000-2-2-2220000000022000000220000-2-2-2-20000000000000000
χ18222222222222222222-2-2-2-22222-2-2-20000-2-2-22200000000-2-2000000-2-2000022220000000000000000
χ19222222222222-2-2222222222-2-2-2-22-20000-22-2-2-2222222220000000000-2-2-2-200000000000000000000
χ20222222222222-2-2222222222-2-2-2-22-20000-22-2-2-2-2-2-2-2-2-2-2-20000000000222200000000000000000000
χ21222222222222-2-22222-2-2-2-22-2-2-22-2200002-22-2-2000000000000000000000000002200000000-2-20000
χ22222222222222-2-22222-2-2-2-22-2-2-22-2200002-22-2-200000000000000000000000000-2-200000000220000
χ232222222-2-222222-2-22-22222-22222-222222-2-2-2-2-20000000000-2-22-22-200000000000000000000000000
χ242222222-2-222222-2-22-22222-22222-22-2-2-2-2-2-2-2-2-2000000000022-22-2200000000000000000000000000
χ252222222-2-222222-2-22-2-2-2-2-2-2222-22-20000222-2-2000000000000000000000000000000000000002-22-2
χ262222222-2-222222-2-22-2-2-2-2-2-2222-22-20000222-2-200000000000000000000000000000000000000-22-22
χ272222222-2-2222-2-2-2-22-22222-2-2-2-2-2-2-200002-222200000000000000000000000000002-22-20000000000
χ282222222-2-2222-2-2-2-22-22222-2-2-2-2-2-2-200002-22220000000000000000000000000000-22-220000000000
χ292222222-2-2222-2-2-2-22-2-2-2-2-2-2-2-2-22220000-22-222000000000000000000000000000000002i−2i2i−2i000000
χ302222222-2-2222-2-2-2-22-2-2-2-2-2-2-2-2-22220000-22-22200000000000000000000000000000000−2i2i−2i2i000000
χ3122222-2-2222-2-222222-222-2-2-22-2-222-200002-2-2-22000000000000000000000000002-200000000-220000
χ3222222-2-2222-2-222222-222-2-2-22-2-222-200002-2-2-2200000000000000000000000000-22000000002-20000
χ3322222-2-2222-2-222222-2-2-222-22-2-2-2-220000-222-222222-2-2-2-20000000000-2-22200000000000000000000
χ3422222-2-2222-2-222222-2-2-222-22-2-2-2-220000-222-22-2-2-2-22222000000000022-2-200000000000000000000
χ3522222-2-2222-2-2-2-2222-222-2-2-2-222-2220000-2-222-20000000022000000-2-20000-2-2220000000000000000
χ3622222-2-2222-2-2-2-2222-222-2-2-2-222-2220000-2-222-200000000-2-200000022000022-2-20000000000000000
χ3722222-2-2-2-22-2-222-2-22222-2-222-2-22-2-20000-2222-2000000000000000000000000000000002i−2i−2i2i000000
χ3822222-2-2-2-22-2-222-2-22222-2-222-2-22-2-20000-2222-200000000000000000000000000000000−2i2i2i−2i000000
χ3922222-2-2-2-22-2-222-2-222-2-22222-2-2-22200002-2-22-200000000000000000000000000002-2-220000000000
χ4022222-2-2-2-22-2-222-2-222-2-22222-2-2-22200002-2-22-20000000000000000000000000000-222-20000000000
χ4122222-2-2-2-22-2-2-2-2-2-22222-2-22-222-2-22000022-2-22000000000000000000000000000000000000002-2-22
χ4222222-2-2-2-22-2-2-2-2-2-22222-2-22-222-2-22000022-2-2200000000000000000000000000000000000000-222-2
χ4322222-2-2-2-22-2-2-2-2-2-222-2-2222-22222-222-2-2-2-22-220000000000-222-2-2200000000000000000000000000
χ4422222-2-2-2-22-2-2-2-2-2-222-2-2222-22222-2-2-222-2-22-2200000000002-2-222-200000000000000000000000000
χ45444444444-4-4-400-4-4-4-400004000000222200000000000000022-2-2-2-200000000000000000000000000
χ46444444444-4-4-400-4-4-4-400004000000-2-2-2-2000000000000000-2-2222200000000000000000000000000
χ474444444-4-4-4-4-40044-440000-40000002222000000000000000-2-2-22-2200000000000000000000000000
χ484444444-4-4-4-4-40044-440000-4000000-2-2-2-2000000000000000222-22-200000000000000000000000000
χ4944444-4-444-44400-4-4-440000-400000022-2-20000000000000002-2-2-22200000000000000000000000000
χ5044444-4-444-44400-4-4-440000-4000000-2-222000000000000000-2222-2-200000000000000000000000000
χ5144444-4-4-4-4-4440044-4-40000400000022-2-2000000000000000-22-222-200000000000000000000000000
χ5244444-4-4-4-4-4440044-4-400004000000-2-2220000000000000002-22-2-2200000000000000000000000000
χ5344-44-44-40044-44400-4000000-44-40000000000002i2i−2i−2i2i2i−2i−2i00000000002i−2i2i−2i00000000000000000000
χ5444-44-44-40044-44400-4000000-44-4000000000000−2i−2i2i2i−2i−2i2i2i0000000000−2i2i−2i2i00000000000000000000
χ5544-44-44-40044-4-4-400-40000004-440000000000002i2i−2i−2i2i2i−2i−2i0000000000−2i2i−2i2i00000000000000000000
χ5644-44-44-40044-4-4-400-40000004-44000000000000−2i−2i2i2i−2i−2i2i2i00000000002i−2i2i−2i00000000000000000000
χ5744-44-44-400-4-440000404-44-40000000000000000000000002-20000002-200002-22-20000000000000000
χ5844-44-44-400-4-440000404-44-4000000000000000000000000-22000000-220000-22-220000000000000000
χ5944-44-44-400-4-44000040-44-440000000000000000000000002-20000002-20000-22-220000000000000000
χ6044-44-44-400-4-44000040-44-44000000000000000000000000-22000000-2200002-22-20000000000000000
χ6144-44-4-44004-444400-4000000-4-440000000000002i2i−2i−2i−2i−2i2i2i0000000000−2i2i2i−2i00000000000000000000
χ6244-44-4-44004-444400-4000000-4-44000000000000−2i−2i2i2i2i2i−2i−2i00000000002i−2i−2i2i00000000000000000000
χ6344-44-4-44004-44-4-400-400000044-40000000000002i2i−2i−2i−2i−2i2i2i00000000002i−2i−2i2i00000000000000000000
χ6444-44-4-44004-44-4-400-400000044-4000000000000−2i−2i2i2i2i2i−2i−2i0000000000−2i2i2i−2i00000000000000000000
χ6544-44-4-4400-44-40000404-4-440000000000000000000000002-2000000-220000-222-20000000000000000
χ6644-44-4-4400-44-40000404-4-44000000000000000000000000-220000002-200002-2-220000000000000000
χ6744-44-4-4400-44-4000040-444-40000000000000000000000002-2000000-2200002-2-220000000000000000
χ6844-44-4-4400-44-4000040-444-4000000000000000000000000-220000002-20000-222-20000000000000000
χ69888-8-8008-80000000000000000000000000000000004i−4i4i−4i0000000000000000000000000000000000
χ70888-8-8008-8000000000000000000000000000000000−4i4i−4i4i0000000000000000000000000000000000
χ71888-8-800-88000000000000000000000000000004i−4i4i−4i00000000000000000000000000000000000000
χ72888-8-800-8800000000000000000000000000000−4i4i−4i4i00000000000000000000000000000000000000
χ7388-8-880000000008-8000000000000000000000000004-4-440000000000000000000000000000000000
χ7488-8-880000000008-800000000000000000000000000-444-40000000000000000000000000000000000
χ7588-8-88000000000-8800000000000000000000004-4-4400000000000000000000000000000000000000
χ7688-8-88000000000-880000000000000000000000-444-400000000000000000000000000000000000000
χ7716-1600000000008-80000000000000004-44-400000000000000000000000000000000000000000000000
χ7816-1600000000008-8000000000000000-44-4400000000000000000000000000000000000000000000000
χ7916-160000000000-880000000000000004-4-4400000000000000000000000000000000000000000000000
χ8016-160000000000-88000000000000000-444-400000000000000000000000000000000000000000000000

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