Finite Group Databasebeta

← Group #125254

Character table — Group #125254

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444488888888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ9111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222222222222222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-22222-2-2-2-22222-2-222-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2222200000000000000000000000000000000
χ21222-2-22-2-22-22-22i2i−2i−2i2i−2i0000000022-2-200002i−2ii2i2−i2−i222−2−222−2−2i2i2−i2−i20000000000000000
χ22222-2-22-2-22-22-22i2i−2i−2i2i−2i0000000022-2-200002i−2i−i2−i2i2i2−2−222−2−222−i2−i2i2i20000000000000000
χ23222-2-22-2-22-22-22i2i−2i−2i2i−2i00000000-2-2220000−2i2i22−2−2−i2−i2i2i2i2i2−i2−i2−2−2220000000000000000
χ24222-2-22-2-22-22-22i2i−2i−2i2i−2i00000000-2-2220000−2i2i−2−222i2i2−i2−i2−i2−i2i2i222−2−20000000000000000
χ25222-2-22-2-22-22-2−2i−2i2i2i−2i2i0000000022-2-20000−2i2ii2i2−i2−i2−2−222−2−222i2i2−i2−i20000000000000000
χ26222-2-22-2-22-22-2−2i−2i2i2i−2i2i0000000022-2-20000−2i2i−i2−i2i2i222−2−222−2−2−i2−i2i2i20000000000000000
χ27222-2-22-2-22-22-2−2i−2i2i2i−2i2i00000000-2-22200002i−2i22−2−2i2i2−i2−i2−i2−i2i2i2−2−2220000000000000000
χ28222-2-22-2-22-22-2−2i−2i2i2i−2i2i00000000-2-22200002i−2i−2−222−i2−i2i2i2i2i2−i2−i222−2−20000000000000000
χ29222-2-22-2-2-22-222i2i−2i−2i−2i2i22-2-22i2i−2i−2i00000000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ30222-2-22-2-2-22-222i2i−2i−2i−2i2i22-2-22i2i−2i−2i0000000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ31222-2-22-2-2-22-222i2i−2i−2i−2i2i-2-222−2i−2i2i2i00000000000000000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i
χ32222-2-22-2-2-22-222i2i−2i−2i−2i2i-2-222−2i−2i2i2i0000000000000000000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i
χ33222-2-22-2-2-22-22−2i−2i2i2i2i−2i22-2-2−2i−2i2i2i00000000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ34222-2-22-2-2-22-22−2i−2i2i2i2i−2i22-2-2−2i−2i2i2i0000000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ35222-2-22-2-2-22-22−2i−2i2i2i2i−2i-2-2222i2i−2i−2i00000000000000000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i
χ36222-2-22-2-2-22-22−2i−2i2i2i2i−2i-2-2222i2i−2i−2i0000000000000000000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i
χ372-2222-2-2-22-2-2200000000002i−2i2i−2i2i−2i2i−2i2-2000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000
χ382-2222-2-2-22-2-2200000000002i−2i2i−2i2i−2i2i−2i2-200000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000
χ392-2222-2-2-22-2-2200000000002i−2i2i−2i−2i2i−2i2i-2200002ζ−2ζ2ζ−2ζ000000002ζ3−2ζ32ζ3−2ζ30000000000000000
χ402-2222-2-2-22-2-2200000000002i−2i2i−2i−2i2i−2i2i-220000−2ζ2ζ−2ζ2ζ00000000−2ζ32ζ3−2ζ32ζ30000000000000000
χ412-2222-2-2-22-2-220000000000−2i2i−2i2i2i−2i2i−2i-2200002ζ3−2ζ32ζ3−2ζ3000000002ζ−2ζ2ζ−2ζ0000000000000000
χ422-2222-2-2-22-2-220000000000−2i2i−2i2i2i−2i2i−2i-220000−2ζ32ζ3−2ζ32ζ300000000−2ζ2ζ−2ζ2ζ0000000000000000
χ432-2222-2-2-22-2-220000000000−2i2i−2i2i−2i2i−2i2i2-2000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ442-2222-2-2-22-2-220000000000−2i2i−2i2i−2i2i−2i2i2-200000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ452-22-2-2-22222-2-20000002i−2i2i−2i00002i−2i−2i2i002-2001+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i0000000000000000
χ462-22-2-2-22222-2-20000002i−2i2i−2i00002i−2i−2i2i002-200−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i0000000000000000
χ472-22-2-2-22222-2-20000002i−2i2i−2i0000−2i2i2i−2i00-22001−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i0000000000000000
χ482-22-2-2-22222-2-20000002i−2i2i−2i0000−2i2i2i−2i00-2200−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i0000000000000000
χ492-22-2-2-22222-2-2000000−2i2i−2i2i00002i−2i−2i2i00-22001+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i0000000000000000
χ502-22-2-2-22222-2-2000000−2i2i−2i2i00002i−2i−2i2i00-2200−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i0000000000000000
χ512-22-2-2-22222-2-2000000−2i2i−2i2i0000−2i2i2i−2i002-2001−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i0000000000000000
χ522-22-2-2-22222-2-2000000−2i2i−2i2i0000−2i2i2i−2i002-200−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i0000000000000000
χ5344444444-4-4-4-44444-4-400000000000000000000000000000000000000000000000000
χ5444444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ5544-44-4-44-400004-44-400000000000000000000000000000000000000002i−2i2i−2i00000000
χ5644-44-4-44-400004-44-40000000000000000000000000000000000000000−2i2i−2i2i00000000
χ5744-44-4-44-40000-44-4400000000000000000000000000000000000000002i−2i−2i2i00000000
χ5844-44-4-44-40000-44-440000000000000000000000000000000000000000−2i2i2i−2i00000000
χ5944-4-44-4-4400004i−4i−4i4i0000000000000000000000000000000000002-22i−2i000000000000
χ6044-4-44-4-4400004i−4i−4i4i000000000000000000000000000000000000-22−2i2i000000000000
χ6144-4-44-4-440000−4i4i4i−4i0000000000000000000000000000000000002-2−2i2i000000000000
χ6244-4-44-4-440000−4i4i4i−4i000000000000000000000000000000000000-222i−2i000000000000
χ634-4444-4-4-4-444-40000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ644-4444-4-4-4-444-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ654-44-4-4-444-4-44400000000004-4-44000000000000000000000000000000000000000000
χ664-44-4-4-444-4-4440000000000-444-4000000000000000000000000000000000000000000
χ678-8-88-88-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

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