Finite Group Databasebeta

← Group #72268792

Character table — Group #72268792

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222444488881616161616161616161616161616161616161616161616163232646464646464646464646464646464646464646464646464
order12222222222222444422224444444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111ii−i−iii−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111−i−iii−i−iii-1-111-1-111ii−i−iii−i−i
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1
χ172222222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2000000000000000000000000
χ182222222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2000000000000000000000000
χ19222222222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ20222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2000000000000000000000000
χ2144444444444444-4-4-4-44-44-40000000000000000000000000000000000000000000000
χ2244444444444444-4-4-4-4-44-440000000000000000000000000000000000000000000000
χ234444444444-4-4-4-444-4-40000000000000000000044-4-400000000000000000000000000
χ244444444444-4-4-4-444-4-400000000000000000000-4-44400000000000000000000000000
χ254444444444-4-4-4-4-4-444000000000000000044-4-4000000000000000000000000000000
χ264444444444-4-4-4-4-4-4440000000000000000-4-444000000000000000000000000000000
χ274-44-4444-4-4-444-4-40000040-400000000000000000000002-22-200000000000000000000
χ284-44-4444-4-4-444-4-40000040-40000000000000000000000-22-2200000000000000000000
χ294-44-4444-4-4-444-4-400000-40400000000000000000000002i−2i−2i2i00000000000000000000
χ304-44-4444-4-4-444-4-400000-4040000000000000000000000−2i2i2i−2i00000000000000000000
χ314-44-4444-4-4-4-4-444000040-40000000000000000000000000002-22-20000000000000000
χ324-44-4444-4-4-4-4-444000040-4000000000000000000000000000-22-220000000000000000
χ334-44-4444-4-4-4-4-4440000-4040000000000000000000000000002i−2i−2i2i0000000000000000
χ344-44-4444-4-4-4-4-4440000-404000000000000000000000000000−2i2i2i−2i0000000000000000
χ354-44-44-4-444-40000004-40000000000000000004i−4i000000000000002ζ−2ζ002ζ3−2ζ30000000000
χ364-44-44-4-444-40000004-40000000000000000004i−4i00000000000000−2ζ2ζ00−2ζ32ζ30000000000
χ374-44-44-4-444-40000004-4000000000000000000−4i4i000000000000002ζ3−2ζ3002ζ−2ζ0000000000
χ384-44-44-4-444-40000004-4000000000000000000−4i4i00000000000000−2ζ32ζ300−2ζ2ζ0000000000
χ394-44-44-4-444-4000000-4400000000000000004i−4i0000000000000000002ζ−2ζ002ζ3−2ζ300000000
χ404-44-44-4-444-4000000-4400000000000000004i−4i000000000000000000−2ζ2ζ00−2ζ32ζ300000000
χ414-44-44-4-444-4000000-440000000000000000−4i4i0000000000000000002ζ3−2ζ3002ζ−2ζ00000000
χ424-44-44-4-444-4000000-440000000000000000−4i4i000000000000000000−2ζ32ζ300−2ζ2ζ00000000
χ434-44-4-44-44-4400004-40000000000000000000000004i−4i0000000000000000002ζ−2ζ00002ζ3−2ζ3
χ444-44-4-44-44-4400004-40000000000000000000000004i−4i000000000000000000−2ζ2ζ0000−2ζ32ζ3
χ454-44-4-44-44-4400004-4000000000000000000000000−4i4i0000000000000000002ζ3−2ζ300002ζ−2ζ
χ464-44-4-44-44-4400004-4000000000000000000000000−4i4i000000000000000000−2ζ32ζ30000−2ζ2ζ
χ474-44-4-44-44-440000-4400000000000000000000004i−4i00000000000000000000002ζ−2ζ2ζ3−2ζ300
χ484-44-4-44-44-440000-4400000000000000000000004i−4i0000000000000000000000−2ζ2ζ−2ζ32ζ300
χ494-44-4-44-44-440000-440000000000000000000000−4i4i00000000000000000000002ζ3−2ζ32ζ−2ζ00
χ504-44-4-44-44-440000-440000000000000000000000−4i4i0000000000000000000000−2ζ32ζ3−2ζ2ζ00
χ5188888-8-8-8-880000000000000000000044-4-40000000000000000000000000000000000
χ5288888-8-8-8-8800000000000000000000-4-4440000000000000000000000000000000000
χ538888-88-8-88-8000000000000000044-4-400000000000000000000000000000000000000
χ548888-88-8-88-80000000000000000-4-44400000000000000000000000000000000000000
χ558888-8-888-8-800000000000044-4-4000000000000000000000000000000000000000000
χ568888-8-888-8-8000000000000-4-444000000000000000000000000000000000000000000
χ578-88-8-8-88-888000000000000000000000000000000004i−4i000000000000000000000000
χ588-88-8-8-88-88800000000000000000000000000000000−4i4i000000000000000000000000
χ598-8-880000004-44-400000000004-4004-4004-40000000000000000000000000000000000
χ608-8-880000004-44-400000000004-400-4400-440000000000000000000000000000000000
χ618-8-880000004-44-40000000000-44004-400-440000000000000000000000000000000000
χ628-8-880000004-44-40000000000-4400-44004-40000000000000000000000000000000000
χ638-8-88000000-44-44000000004-4004-4004-4000000000000000000000000000000000000
χ648-8-88000000-44-44000000004-400-4400-44000000000000000000000000000000000000
χ658-8-88000000-44-4400000000-44004-400-44000000000000000000000000000000000000
χ668-8-88000000-44-4400000000-4400-44004-4000000000000000000000000000000000000
χ671616-16-160000008-8-88000000000000000000000000000000000000000000000000000000
χ681616-16-16000000-888-8000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.