Finite Group Databasebeta

← Group #72334808

Character table — Group #72334808

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1122222224444444444888888888888888881616161632323232323232323232323232323232323232323232323264646464646464646464646464646464
order12222222222222222222222222222244444422244444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i
χ101111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iii−i−iii−i−iii
χ111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii
χ121111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i
χ131111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222-2-2-2-2222-2-2-2-2-2-222-2-2-2-2-2-2222-20000000000000000000000002-22-2000000000000
χ18222222222222222-2-2-2-2222-2-2-2-2-2-222-2-2-2-2-2-2222-2000000000000000000000000-22-22000000000000
χ19222222222222222-2-2-2-2222-2-2-2-2-2-2-2-2222222-2-2-220000000000000000000000002i−2i−2i2i000000000000
χ20222222222222222-2-2-2-2222-2-2-2-2-2-2-2-2222222-2-2-22000000000000000000000000−2i2i2i−2i000000000000
χ2122222222222-2-2-2-222222-2-222-2-2-2-22222-2-2-2-22-2-220000000022-2-20000000022-2-20000000000000000
χ2222222222222-2-2-2-222222-2-222-2-2-2-22222-2-2-2-22-2-2200000000-2-22200000000-2-2220000000000000000
χ2322222222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-22222-222-20000000022-2-200000000-2-2220000000000000000
χ2422222222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-22222-222-200000000-2-2220000000022-2-20000000000000000
χ2522222222222-2-2-2-2-2-2-2-22-2-2-2-2222222-2-222222-2-2-20000000000000000000000000000000000002i−2i2i−2i
χ2622222222222-2-2-2-2-2-2-2-22-2-2-2-2222222-2-222222-2-2-2000000000000000000000000000000000000−2i2i−2i2i
χ2722222222222-2-2-2-2-2-2-2-22-2-2-2-22222-2-222-2-2-2-2-22220000000000000000000000000000000000002-2-22
χ2822222222222-2-2-2-2-2-2-2-22-2-2-2-22222-2-222-2-2-2-2-2222000000000000000000000000000000000000-222-2
χ29222222222-2-222-2-22222-22-2-2-222-2-222-2-222-2-2-22-22000022-2-20000000022-2-200000000000000000000
χ30222222222-2-222-2-22222-22-2-2-222-2-222-2-222-2-2-22-220000-2-22200000000-2-22200000000000000000000
χ31222222222-2-222-2-22222-22-2-2-222-2-2-2-222-2-2222-22-2000022-2-200000000-2-22200000000000000000000
χ32222222222-2-222-2-22222-22-2-2-222-2-2-2-222-2-2222-22-20000-2-2220000000022-2-200000000000000000000
χ33222222222-2-222-2-2-2-2-2-2-22-222-2-2222222-2-222-22-2-2000000000000000000000000000000002i−2i2i−2i0000
χ34222222222-2-222-2-2-2-2-2-2-22-222-2-2222222-2-222-22-2-200000000000000000000000000000000−2i2i−2i2i0000
χ35222222222-2-222-2-2-2-2-2-2-22-222-2-222-2-2-2-222-2-22-222000000000000000000000000000000002-2-220000
χ36222222222-2-222-2-2-2-2-2-2-22-222-2-222-2-2-2-222-2-22-22200000000000000000000000000000000-222-20000
χ37222222222-2-2-2-2222222-2-22-2-2-2-22222-2-2-2-222-2-22222-2-20000000022-2-2000000000000000000000000
χ38222222222-2-2-2-2222222-2-22-2-2-2-22222-2-2-2-222-2-222-2-22200000000-2-222000000000000000000000000
χ39222222222-2-2-2-2222222-2-22-2-2-2-222-2-22222-2-222-2-222-2-200000000-2-222000000000000000000000000
χ40222222222-2-2-2-2222222-2-22-2-2-2-222-2-22222-2-222-2-2-2-2220000000022-2-2000000000000000000000000
χ41222222222-2-2-2-222-2-2-2-2-2-222222-2-2222222-2-2-2-22-200000000000000000000000000002i−2i2i−2i00000000
χ42222222222-2-2-2-222-2-2-2-2-2-222222-2-2222222-2-2-2-22-20000000000000000000000000000−2i2i−2i2i00000000
χ43222222222-2-2-2-222-2-2-2-2-2-222222-2-2-2-2-2-2-2-22222-2200000000000000000000000000002-2-2200000000
χ44222222222-2-2-2-222-2-2-2-2-2-222222-2-2-2-2-2-2-2-22222-220000000000000000000000000000-222-200000000
χ4544444-4-4-4-400004444-4-400-400004-4000000000000004i−4i000000000000000000000000000000000000
χ4644444-4-4-4-400004444-4-400-400004-400000000000000−4i4i000000000000000000000000000000000000
χ4744444-4-4-4-4000044-4-44400-40000-44000000000000000000000000004-4000000000000000000000000
χ4844444-4-4-4-4000044-4-44400-40000-4400000000000000000000000000-44000000000000000000000000
χ4944444-4-4-4-40000-4-444-4-40040000-440000000000004i−4i00000000000000000000000000000000000000
χ5044444-4-4-4-40000-4-444-4-40040000-44000000000000−4i4i00000000000000000000000000000000000000
χ5144444-4-4-4-40000-4-4-4-44400400004-40000000000000000000000004-400000000000000000000000000
χ5244444-4-4-4-40000-4-4-4-44400400004-4000000000000000000000000-4400000000000000000000000000
χ53444-4-444-4-40044004-44-40-40004-4000000000000000000004i−4i00000000000000000000000000000000
χ54444-4-444-4-40044004-44-40-40004-400000000000000000000−4i4i00000000000000000000000000000000
χ55444-4-444-4-4004400-44-440-4000-44000000000000000000000000000000004-400000000000000000000
χ56444-4-444-4-4004400-44-440-4000-4400000000000000000000000000000000-4400000000000000000000
χ57444-4-444-4-400-4-4004-44-404000-440000000000000000004i−4i0000000000000000000000000000000000
χ58444-4-444-4-400-4-4004-44-404000-44000000000000000000−4i4i0000000000000000000000000000000000
χ59444-4-444-4-400-4-400-44-44040004-40000000000000000000000000000004-40000000000000000000000
χ60444-4-444-4-400-4-400-44-44040004-4000000000000000000000000000000-440000000000000000000000
χ61444-4-4-4-4444400004-4-44-4004-4000000000000000000000000000000000000004-40000000000000000
χ62444-4-4-4-4444400004-4-44-4004-400000000000000000000000000000000000000-440000000000000000
χ63444-4-4-4-444440000-444-4-400-44000000000000000000000000004i−4i0000000000000000000000000000
χ64444-4-4-4-444440000-444-4-400-4400000000000000000000000000−4i4i0000000000000000000000000000
χ65444-4-4-4-444-4-400004-4-44400-440000000000000000000000000000000000004-4000000000000000000
χ66444-4-4-4-444-4-400004-4-44400-44000000000000000000000000000000000000-44000000000000000000
χ67444-4-4-4-444-4-40000-444-44004-40000000000000000000000004i−4i000000000000000000000000000000
χ68444-4-4-4-444-4-40000-444-44004-4000000000000000000000000−4i4i000000000000000000000000000000
χ6988-88-88-88-800000000000000000000000008-800000000000000000000000000000000000000000000
χ7088-88-88-88-80000000000000000000000000-8800000000000000000000000000000000000000000000
χ7188-88-8-88-88000000000000000000000008-80000000000000000000000000000000000000000000000
χ7288-88-8-88-8800000000000000000000000-880000000000000000000000000000000000000000000000
χ7388-8-888-8-8800000000000000000008-800000000000000000000000000000000000000000000000000
χ7488-8-888-8-880000000000000000000-8800000000000000000000000000000000000000000000000000
χ7588-8-88-888-80000000000000000000008-8000000000000000000000000000000000000000000000000
χ7688-8-88-888-8000000000000000000000-88000000000000000000000000000000000000000000000000
χ7716-1600000008-88-88-800000000000000000000000000000000000000000000000000000000000000000
χ7816-1600000008-8-88-8800000000000000000000000000000000000000000000000000000000000000000
χ7916-160000000-888-8-8800000000000000000000000000000000000000000000000000000000000000000
χ8016-160000000-88-888-800000000000000000000000000000000000000000000000000000000000000000

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