Finite Group Databasebeta

← Group #72338841

Character table — Group #72338841

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size112224444444488888888888881616161616161616161616161616161616161616161616323232323232323232323232323232323232323232326464646464128128128128
order12222224444442244488888888222222224444444888888882244444444444488888888888884488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1111-1-111111111-1-1-1-11-1-11111111-1-1-1-111-1-1-1-1-1-111111-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111111111111-1-11-1-1-1-11111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1111-1-111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-1111-1-11111-1-1-1-111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111-1-1-1-11111-1-1-11111-1-111
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-11111111-1-11-1-1-1-1-1-111-1-1-1-1-1-111-1111111-1-1
χ9111111111-1-111-1-1-1111111111111-1-11111-1111-111-1-1-1-11111-1-1-11-1-111-1-111-1-111-1-1-1-111-111-1-11-11-1
χ10111111111-1-111-1-1-1111111111111-1-1-1-111-1-1-11-111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-111111111-1-1-111-1-1-11-11
χ11111111111-1-111-1-1-11111111111-1-1111111-1111-111-1-1-1-11111-1-1-1-11-1-1-11111-1-111-1-1-1-111-1-1-111-11-11
χ12111111111-1-111-1-1-11111111111-1-111-1-111-1-1-11-111-1-1-1-1-1-1-1-1-111-11-1-1-111-1-111111111-1-1-1-1-1111-11-1
χ13111111111-1-111-1-1-111-1-1-1-1-1-1-1-111-1-11111-1111-1111111-1-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-11-1-1111-1-11
χ14111111111-1-111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-11-11111111111-1-1-11-1-111-1-1-1-1-1-1-1-11111111-1-111-111-1
χ15111111111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1111-1111111-1-1-1-1-111-11-1-1-1111111-1-1-1-1-1-1-1-1111-1-1-111-1
χ16111111111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11-11111111111-1-1-1-11-1-1-111-1-1-1-1-1-1111111111-1-11-1-11
χ1722222222222222222222222222000000-2-220022-2-222220000-20000-200000000-2-2000000-200000000
χ18222222222222222222-2-2-2-2-2-2-2-2000000-2-220022-2-2-2-2-2-20000-20000-20000000022000000200000000
χ192222222222222-2-22-2-200000000000000-2-2-200-222200002222-2-2-200200000022000000-2-2000000000
χ202222222222222-2-22-2-200000000000000-2-2-200-22220000-2-2-2-2-222002000000-2-200000022000000000
χ212222222222222-2-22-2-20000000000002222-222-22-2-20000000020000-20000-2-2000022-2-200000000000
χ222222222222222-2-22-2-2000000000000-2-222-2-2-2-22-2-20000000020000-20000220000-2-22200000000000
χ23222222222-2-22222-2-2-200000000000000-2-2200-2-2220000222222200-2000000-2-2000000-2-2000000000
χ24222222222-2-22222-2-2-200000000000000-2-2200-2-2220000-2-2-2-22-2-200-20000002200000022000000000
χ25222222222-2-22222-2-2-20000000000002222222-2-2-2-200000000-2000020000-2-20000-2-22200000000000
χ26222222222-2-22222-2-2-2000000000000-2-2222-2-2-2-2-2-200000000-200002000022000022-2-200000000000
χ27222222222-2-222-2-2-22222222222000000-2-2-2002-2-2-2-2-2-2-2000020000200000000-2-2000000200000000
χ28222222222-2-222-2-2-222-2-2-2-2-2-2-2-2000000-2-2-2002-2-2-2222200002000020000000022000000-200000000
χ292222222-2-200-2-2000-2-22i2i2i2i−2i−2i−2i−2i0022002-2000202-20000000000002000-2-200002i−2i0000000002i−2i0000
χ302222222-2-200-2-2000-2-22i2i2i2i−2i−2i−2i−2i00-2-2002-2000202-2000000000000-20002200002i−2i000000000−2i2i0000
χ312222222-2-200-2-2000-2-22i2i2i2i−2i−2i−2i−2i220000-2200020-2200000000000200-2-2000000−2i2i00000002i−2i000000
χ322222222-2-200-2-2000-2-22i2i2i2i−2i−2i−2i−2i-2-20000-2200020-2200000000000-20022000000−2i2i0000000−2i2i000000
χ332222222-2-200-2-2000-2-2−2i−2i−2i−2i2i2i2i2i0022002-2000202-20000000000002000-2-20000−2i2i000000000−2i2i0000
χ342222222-2-200-2-2000-2-2−2i−2i−2i−2i2i2i2i2i00-2-2002-2000202-2000000000000-2000220000−2i2i0000000002i−2i0000
χ352222222-2-200-2-2000-2-2−2i−2i−2i−2i2i2i2i2i220000-2200020-2200000000000200-2-20000002i−2i0000000−2i2i000000
χ362222222-2-200-2-2000-2-2−2i−2i−2i−2i2i2i2i2i-2-20000-2200020-2200000000000-200220000002i−2i00000002i−2i000000
χ374444444-4-400-4-400044000000000000004-4000-40-44000000000000000000000000000000000000000
χ384444444-4-400-4-40004400000000000000-44000-404-4000000000000000000000000000000000000000
χ3944444-4-44-4004-4440000000000022220000-400000000000000000-2-202-22-2000000000000000000000
χ4044444-4-44-4004-44400000000000-2-2-2-20000-400000000000000000220-22-22000000000000000000000
χ4144444-4-44-4004-4-4-40000000000022-2-20000400000000000000000-2202-2-22000000000000000000000
χ4244444-4-44-4004-4-4-400000000000-2-22200004000000000000000002-20-222-2000000000000000000000
χ4344444-4-4-4444-440040000000000222200000000-40000000000000-2-20-22-22000000000000000000000
χ4444444-4-4-4444-440040000000000-2-2-2-200000000-400000000000002202-22-2000000000000000000000
χ4544444-4-4-44-4-4-4400-4000000000022-2-20000000040000000000000-220-222-2000000000000000000000
χ4644444-4-4-44-4-4-4400-40000000000-2-22200000000400000000000002-202-2-22000000000000000000000
χ47444-4-44-40000000004i−4i2+2i2+2i−2−2i−2−2i2−2i2−2i−2+2i−2+2i000022000-2-20000000022-2-200000000002i−2i000000002i−2i000000000
χ48444-4-44-40000000004i−4i2+2i2+2i−2−2i−2−2i2−2i2−2i−2+2i−2+2i0000-2-20002200000000-2-2220000000000−2i2i00000000−2i2i000000000
χ49444-4-44-40000000004i−4i−2−2i−2−2i2+2i2+2i−2+2i−2+2i2−2i2−2i000022000-2-200000000-2-22200000000002i−2i00000000−2i2i000000000
χ50444-4-44-40000000004i−4i−2−2i−2−2i2+2i2+2i−2+2i−2+2i2−2i2−2i0000-2-2000220000000022-2-20000000000−2i2i000000002i−2i000000000
χ51444-4-44-4000000000−4i4i2−2i2−2i−2+2i−2+2i2+2i2+2i−2−2i−2−2i000022000-2-20000000022-2-20000000000−2i2i00000000−2i2i000000000
χ52444-4-44-4000000000−4i4i2−2i2−2i−2+2i−2+2i2+2i2+2i−2−2i−2−2i0000-2-20002200000000-2-22200000000002i−2i000000002i−2i000000000
χ53444-4-44-4000000000−4i4i−2+2i−2+2i2−2i2−2i−2−2i−2−2i2+2i2+2i000022000-2-200000000-2-2220000000000−2i2i000000002i−2i000000000
χ54444-4-44-4000000000−4i4i−2+2i−2+2i2−2i2−2i−2−2i−2−2i2+2i2+2i0000-2-2000220000000022-2-200000000002i−2i00000000−2i2i000000000
χ5544-44-4000-4440400-4002-22-22-22-200002-20002-2000022-2-22-22-20000000000002-2002-20000000000000
χ5644-44-4000-4440400-4002-22-22-22-20000-22000-22000022-2-2-22-22000000000000-2200-220000000000000
χ5744-44-4000-4440400-400-22-22-22-2200002-20002-20000-2-222-22-22000000000000-22002-20000000000000
χ5844-44-4000-4440400-400-22-22-22-220000-22000-220000-2-2222-22-20000000000002-200-220000000000000
χ5944-44-4000-4-4-404004002-22-22-22-200002-20002-20000-2-2222-22-2000000000000-2200-220000000000000
χ6044-44-4000-4-4-404004002-22-22-22-20000-22000-220000-2-222-22-220000000000002-2002-20000000000000
χ6144-44-4000-4-4-40400400-22-22-22-2200002-20002-2000022-2-2-22-220000000000002-200-220000000000000
χ6244-44-4000-4-4-40400400-22-22-22-220000-22000-22000022-2-22-22-2000000000000-22002-20000000000000
χ6344-4-4400-4000404-40002-2-222-2-2200002-2000-2200002-22-22-2-2202-20000000000000002-200000000000
χ6444-4-4400-4000404-40002-2-222-2-220000-220002-200002-22-2-222-20-22000000000000000-2200000000000
χ6544-4-4400-4000404-4000-222-2-222-200002-2000-220000-22-22-222-20-220000000000000002-200000000000
χ6644-4-4400-4000404-4000-222-2-222-20000-220002-20000-22-222-2-2202-2000000000000000-2200000000000
χ6744-4-4400-400040-440002-2-222-2-2200002-2000-220000-22-222-2-220-22000000000000000-2200000000000
χ6844-4-4400-400040-440002-2-222-2-220000-220002-20000-22-22-222-202-20000000000000002-200000000000
χ6944-4-4400-400040-44000-222-2-222-200002-2000-2200002-22-2-222-202-2000000000000000-2200000000000
χ7044-4-4400-400040-44000-222-2-222-20000-220002-200002-22-22-2-220-220000000000000002-200000000000
χ71888-8-8-8800000000000000000000000000000000004-4-4400000000000000000000000000000000000
χ72888-8-8-880000000000000000000000000000000000-444-400000000000000000000000000000000000
χ7388-88-80008000-8000004i−4i4i−4i−4i4i−4i4i000000000000000000000000000000000000000000000000000000
χ7488-88-80008000-800000−4i4i−4i4i4i−4i4i−4i000000000000000000000000000000000000000000000000000000
χ7588-8-88008000-80000004i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ7688-8-88008000-8000000−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ7716-1600000008-80000000000000004-44-400000000000000000000000000000000000000000000000000
χ7816-1600000008-8000000000000000-44-4400000000000000000000000000000000000000000000000000
χ7916-160000000-880000000000000004-4-4400000000000000000000000000000000000000000000000000
χ8016-160000000-88000000000000000-444-400000000000000000000000000000000000000000000000000

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