Finite Group Databasebeta

← Group #72240518

Character table — Group #72240518

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11222222244444444444444888888816161616161616161616161616161616161616161616161632323232323232323232323232323232
order1222244442222222244444422244442222224444444444888888884444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ911111-1-1-1-111-1-111-1-111-1-1-1-11-1-1111-111-1-11-11-111-1-111-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−iii−i−i
χ1011111-1-1-1-111-1-111-1-111-1-1-1-11-1-1111-111-1-11-11-111-1-111-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii−i−iii
χ1111111-1-1-1-111-1-111-1-111-1-1-1-11-1-1111-111-1-1-11-1111-1-1-1-111iiii−i−i−i−i-1-111ii−i−i−i−iii−i−iii
χ1211111-1-1-1-111-1-111-1-111-1-1-1-11-1-1111-111-1-1-11-1111-1-1-1-111−i−i−i−iiiii-1-111−i−iiiii−i−iii−i−i
χ1311111-1-1-1-111-1-111-1-111-1-1-1-11-1-1111-1-1-1111-11-1-1-11111-1-1iiii−i−i−i−i-1-111−i−iii−i−iiiii−i−i
χ1411111-1-1-1-111-1-111-1-111-1-1-1-11-1-1111-1-1-1111-11-1-1-11111-1-1−i−i−i−iiiii-1-111ii−i−iii−i−i−i−iii
χ1511111-1-1-1-111-1-111-1-111-1-1-1-11-1-1111-1-1-111-11-11-1-111-1-111iiii−i−i−i−i11-1-1−i−iiiii−i−i−i−iii
χ1611111-1-1-1-111-1-111-1-111-1-1-1-11-1-1111-1-1-111-11-11-1-111-1-111−i−i−i−iiiii11-1-1ii−i−i−i−iiiii−i−i
χ172222222222222-2-2-2-2-2-2-2-222-2-2222-2-20000000000000000000000000000000000002-22-2
χ182222222222222-2-2-2-2-2-2-2-222-2-2222-2-2000000000000000000000000000000000000-22-22
χ1922222222222-2-222-2-2-2-22222-22-2-2-22-2000022220000-2-2-2-2000000000000000000000000
χ2022222222222-2-222-2-2-2-22222-22-2-2-22-20000-2-2-2-200002222000000000000000000000000
χ2122222222222-2-2-2-22222-2-2222-2-2-2-2-22000000000000000022-2-222-2-20000000000000000
χ2222222222222-2-2-2-22222-2-2222-2-2-2-2-220000000000000000-2-222-2-2220000000000000000
χ23222222222-2-22222222222-2-2-2-2-22-2-2-222220000-2-2-2-20000000000000000000000000000
χ24222222222-2-22222222222-2-2-2-2-22-2-2-2-2-2-2-2000022220000000000000000000000000000
χ25222222222-2-222-2-2-2-2-2-2-2-2-2-222-22-222000000000000000000000000000000002i−2i2i−2i0000
χ26222222222-2-222-2-2-2-2-2-2-2-2-2-222-22-22200000000000000000000000000000000−2i2i−2i2i0000
χ27222222222-2-2-2-222-2-2-2-222-2-22-22-22-220000000000000000000000002-22-2000000000000
χ28222222222-2-2-2-222-2-2-2-222-2-22-22-22-22000000000000000000000000-22-22000000000000
χ29222222222-2-2-2-2-2-22222-2-2-2-2-222-222-200000000000000000000000000002-22-200000000
χ30222222222-2-2-2-2-2-22222-2-2-2-2-222-222-20000000000000000000000000000-22-2200000000
χ3122222-2-2-2-222222222-2-2-2-2-2-2-2-22-2-22200002-22-20000-2-222000000000000000000000000
χ3222222-2-2-2-222222222-2-2-2-2-2-2-2-22-2-2220000-22-22000022-2-2000000000000000000000000
χ3322222-2-2-2-22222-2-2-2-22222-2-2222-2-2-2-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ3422222-2-2-2-22222-2-2-2-22222-2-2222-2-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ3522222-2-2-2-222-2-2-2-222-2-222-2-2-22-222-220000000000000000000000000000000000002i−2i−2i2i
χ3622222-2-2-2-222-2-2-2-222-2-222-2-2-22-222-22000000000000000000000000000000000000−2i2i2i−2i
χ3722222-2-2-2-2-2-2222222-2-2-2-22222-2-22-2-20000000000000000000000002-2-22000000000000
χ3822222-2-2-2-2-2-2222222-2-2-2-22222-2-22-2-2000000000000000000000000-222-2000000000000
χ3922222-2-2-2-2-2-222-2-2-2-2222222-2-2-2-222200000000000000000000000000002i−2i−2i2i00000000
χ4022222-2-2-2-2-2-222-2-2-2-2222222-2-2-2-22220000000000000000000000000000−2i2i2i−2i00000000
χ4122222-2-2-2-2-2-2-2-222-2-222-2-222-2222-2-2222-2-20000-2-2220000000000000000000000000000
χ4222222-2-2-2-2-2-2-2-222-2-222-2-222-2222-2-22-2-222000022-2-20000000000000000000000000000
χ4322222-2-2-2-2-2-2-2-2-2-222-2-222222-222-22-2000000000000000000000000000000002-2-220000
χ4422222-2-2-2-2-2-2-2-2-2-222-2-222222-222-22-200000000000000000000000000000000-222-20000
χ45444-4-444-4-400004-400004-400000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ46444-4-444-4-400004-400004-40000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ47444-4-444-4-40000-440000-4400000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ48444-4-444-4-40000-440000-440000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ49444-4-4-4-44400004-40000-4400000000000000000000000002-22-2-22-220000000000000000
χ50444-4-4-4-44400004-40000-440000000000000000000000000-22-222-22-20000000000000000
χ51444-4-4-4-4440000-4400004-400000000000000000000000002-2-22-222-20000000000000000
χ52444-4-4-4-4440000-4400004-40000000000000000000000000-222-22-2-220000000000000000
χ5344-44-44-44-40000004-44-400000000000000022-2-200002-22-2000000000000000000000000
χ5444-44-44-44-40000004-44-4000000000000000-2-2220000-22-22000000000000000000000000
χ5544-44-44-44-4000000-44-4400000000000000022-2-20000-22-22000000000000000000000000
χ5644-44-44-44-4000000-44-44000000000000000-2-22200002-22-2000000000000000000000000
χ5744-44-4-44-440000004-4-440000000000000002-2-220000-222-2000000000000000000000000
χ5844-44-4-44-440000004-4-44000000000000000-222-200002-2-22000000000000000000000000
χ5944-44-4-44-44000000-444-40000000000000002-2-2200002-2-22000000000000000000000000
χ6044-44-4-44-44000000-444-4000000000000000-222-20000-222-2000000000000000000000000
χ6144-4-444-4-444-400000000004-400000002-22-200002-22-20000000000000000000000000000
χ6244-4-444-4-444-400000000004-40000000-22-220000-22-220000000000000000000000000000
χ6344-4-444-4-44-440000000000-4400000002-22-20000-22-220000000000000000000000000000
χ6444-4-444-4-44-440000000000-440000000-22-2200002-22-20000000000000000000000000000
χ6544-4-44-444-44-40000000000-4400000002-2-2200002-2-220000000000000000000000000000
χ6644-4-44-444-44-40000000000-440000000-222-20000-222-20000000000000000000000000000
χ6744-4-44-444-4-4400000000004-400000002-2-220000-222-20000000000000000000000000000
χ6844-4-44-444-4-4400000000004-40000000-222-200002-2-220000000000000000000000000000
χ6916-160000000008-8000000000000000000000000000000000000000000000000000000000
χ7016-16000000000-88000000000000000000000000000000000000000000000000000000000

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