Finite Group Databasebeta

← Group #72255980

Character table — Group #72255980

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1122222224444444444888888888161616161616161616161616161616163232323232323232323232323232323232323232
order1222222222222222222222224444224444444444444444444444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111111-1-111-1-1-1-111-1-1-111-1-1111111-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111111-1-111-1-1-1-111-1-1-111-1-1111111-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111111-1-111-1-1-1-111-1-1-111-1-11111-1-111-1-1-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1211111111111-1-111-1-1-1-111-1-1-111-1-11111-1-111-1-1-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1311111111111-1-111-1-1-1-111-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-111ii−i−iii−i−i−i−iii−i−iii
χ1411111111111-1-111-1-1-1-111-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-111−i−iii−i−iiiii−i−iii−i−i
χ1511111111111-1-111-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111-1-111-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222222-2-22-2-2-2-2-2-2000022220000-2-2-2-200000000000000000000
χ182222222222222222222-2-22-2-2-2-2-2-20000-2-2-2-20000222200000000000000000000
χ1922222222222-2-222-2-2-2-2-2-2-222-2-222000022-2-20000-2-22200000000000000000000
χ2022222222222-2-222-2-2-2-2-2-2-222-2-2220000-2-222000022-2-200000000000000000000
χ21222222222-2-222-2-2-2-2-2-222222-2-2-2-20000000000000000000000002i−2i2i−2i00000000
χ22222222222-2-222-2-2-2-2-2-222222-2-2-2-2000000000000000000000000−2i2i−2i2i00000000
χ23222222222-2-222-2-2-2-2-2-2-2-22-2-22222000000000000000000002i−2i2i−2i000000000000
χ24222222222-2-222-2-2-2-2-2-2-2-22-2-2222200000000000000000000−2i2i−2i2i000000000000
χ25222222222-2-2-2-2-2-2222222-2-2-2-2-2220000000000000000000000002-2-2200000000
χ26222222222-2-2-2-2-2-2222222-2-2-2-2-222000000000000000000000000-222-200000000
χ27222222222-2-2-2-2-2-22222-2-2-22222-2-2000000000000000000002-2-22000000000000
χ28222222222-2-2-2-2-2-22222-2-2-22222-2-200000000000000000000-222-2000000000000
χ29222-2-2-2-2222222-2-222-2-22-2-22-22-22-2000000000000000000000000000000002i−2i2i−2i
χ30222-2-2-2-2222222-2-222-2-22-2-22-22-22-200000000000000000000000000000000−2i2i−2i2i
χ31222-2-2-2-2222222-2-222-2-2-22-2-22-22-2200000000000000000000000000002-22-20000
χ32222-2-2-2-2222222-2-222-2-2-22-2-22-22-220000000000000000000000000000-22-220000
χ33222-2-2-2-22222-2-2-2-2-2-2222-22-222-2-22000000000000000000000000000000002-2-22
χ34222-2-2-2-22222-2-2-2-2-2-2222-22-222-2-2200000000000000000000000000000000-222-2
χ35222-2-2-2-22222-2-2-2-2-2-222-2222-2-222-200000000000000000000000000002i−2i−2i2i0000
χ36222-2-2-2-22222-2-2-2-2-2-222-2222-2-222-20000000000000000000000000000−2i2i2i−2i0000
χ37222-2-2-2-222-2-22222-2-2222-2-22-2-22-222-22-2000022-2-2000000000000000000000000
χ38222-2-2-2-222-2-22222-2-2222-2-22-2-22-22-22-220000-2-222000000000000000000000000
χ39222-2-2-2-222-2-22222-2-222-22-2-222-22-200000000000000002-22-20000000000000000
χ40222-2-2-2-222-2-22222-2-222-22-2-222-22-20000000000000000-22-220000000000000000
χ41222-2-2-2-222-2-2-2-22222-2-22-22-22-222-22-22-20000-2-222000000000000000000000000
χ42222-2-2-2-222-2-2-2-22222-2-22-22-22-222-2-22-22000022-2-2000000000000000000000000
χ43222-2-2-2-222-2-2-2-22222-2-2-2222-22-2-2200000000000000002-2-220000000000000000
χ44222-2-2-2-222-2-2-2-22222-2-2-2222-22-2-220000000000000000-222-20000000000000000
χ4544444-4-4-4-44-4004-40000000000000000000000000004i−4i00000000000000000000
χ4644444-4-4-4-44-4004-4000000000000000000000000000−4i4i00000000000000000000
χ4744444-4-4-4-4-4400-4400000000000000000000000004i−4i0000000000000000000000
χ4844444-4-4-4-4-4400-440000000000000000000000000−4i4i0000000000000000000000
χ49444-4-444-4-44-400-44000000000000000004i−4i000000000000000000000000000000
χ50444-4-444-4-44-400-4400000000000000000−4i4i000000000000000000000000000000
χ51444-4-444-4-4-44004-400000000000000000004i−4i0000000000000000000000000000
χ52444-4-444-4-4-44004-40000000000000000000−4i4i0000000000000000000000000000
χ5344-44-44-4-440000004-44-400000000022-2-200002-22-2000000000000000000000000
χ5444-44-44-4-440000004-44-4000000000-2-2220000-22-22000000000000000000000000
χ5544-44-44-4-44000000-44-4400000000022-2-20000-22-22000000000000000000000000
χ5644-44-44-4-44000000-44-44000000000-2-22200002-22-2000000000000000000000000
χ5744-4-44-44-440000004-4-440000000002-2-220000-222-2000000000000000000000000
χ5844-4-44-44-440000004-4-44000000000-222-200002-2-22000000000000000000000000
χ5944-4-44-44-44000000-444-40000000002-2-2200002-2-22000000000000000000000000
χ6044-4-44-44-44000000-444-4000000000-222-20000-222-2000000000000000000000000
χ6188-88-8-888-80000000000000000000000000000000000000000000000000000000
χ6288-8-888-88-80000000000000000000000000000000000000000000000000000000
χ6316-160000000008-8000000000000000000000000000000000000000000000000000
χ6416-16000000000-88000000000000000000000000000000000000000000000000000

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