Finite Group Databasebeta

← Group #97161

Character table — Group #97161

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
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
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11-11111-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-11-1-1-1-11111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11-1-1-1-1-11111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-1-1111-1ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii-1111-1-1-11−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1111-1−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1-11ii−i−i−i−iii
χ1722222222222222222222-2-22222-2-2-2-2-2-222-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-22200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ2122222222-2-2-2-222-2-222-2-22-200002-22-2000000000000000000000002002-20-200000000
χ2222222222-2-2-2-222-2-222-2-22-200002-22-200000000000000000000000-200-220200000000
χ2322222222-2-2-2-222-2-222-2-2-220000-22-220000000000000000000000202-200-2000000000
χ2422222222-2-2-2-222-2-222-2-2-220000-22-220000000000000000000000-20-22002000000000
χ2522222222-2-2-2-2-2-222-2-2222-200002-2-22000000000000000000000020-2200-2000000000
χ2622222222-2-2-2-2-2-222-2-2222-200002-2-220000000000000000000000-202-2002000000000
χ2722222222-2-2-2-2-2-222-2-222-220000-222-200000000000000000000000200-220-200000000
χ2822222222-2-2-2-2-2-222-2-222-220000-222-200000000000000000000000-2002-20200000000
χ29222-2-2-2-2222-2-22i−2i2i−2i2i−2i2i−2i0022-2-20000002i−2i000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ30222-2-2-2-2222-2-22i−2i2i−2i2i−2i2i−2i0022-2-20000002i−2i00000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ31222-2-2-2-2222-2-22i−2i2i−2i2i−2i2i−2i00-2-222000000−2i2i000000000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ32222-2-2-2-2222-2-22i−2i2i−2i2i−2i2i−2i00-2-222000000−2i2i00000000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ33222-2-2-2-2222-2-2−2i2i−2i2i−2i2i−2i2i0022-2-2000000−2i2i000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ34222-2-2-2-2222-2-2−2i2i−2i2i−2i2i−2i2i0022-2-2000000−2i2i00000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ35222-2-2-2-2222-2-2−2i2i−2i2i−2i2i−2i2i00-2-2220000002i−2i000000000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ36222-2-2-2-2222-2-2−2i2i−2i2i−2i2i−2i2i00-2-2220000002i−2i00000000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ372-2-2-222-222-22-200000000222-22-2-2-20000002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ382-2-2-222-222-22-200000000222-22-2-2-20000002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ392-2-2-222-222-22-20000000022-22-22-2-2000000-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ402-2-2-222-222-22-20000000022-22-22-2-2000000-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ412-2-2-222-222-22-200000000-2-22-22-222000000-2222−2−2−2−22222−2−2−2−2220000000000000000
χ422-2-2-222-222-22-200000000-2-22-22-222000000-22−2−22222−2−2−2−22222−2−20000000000000000
χ432-2-2-222-222-22-200000000-2-2-22-22220000002-222−2−2−2−222−2−22222−2−20000000000000000
χ442-2-2-222-222-22-200000000-2-2-22-22220000002-2−2−22222−2−222−2−2−2−2220000000000000000
χ45444-4-4-4-44-4-4444i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000
χ46444-4-4-4-44-4-444−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000
χ4744-444-4-4-40000004400-4-400000000000000002-22-22-22-2000000000000000000000000
χ4844-444-4-4-40000004400-4-40000000000000000-22-22-22-22000000000000000000000000
χ4944-444-4-4-4000000-4-4004400000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ5044-444-4-4-4000000-4-400440000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ5144-4-4-444-40000004i−4i00−4i4i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000
χ5244-4-4-444-40000004i−4i00−4i4i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000
χ5344-4-4-444-4000000−4i4i004i−4i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000
χ5444-4-4-444-4000000−4i4i004i−4i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000
χ554-444-44-4-400004400-4-4000000000000000000000000002-2-222-2-220000000000000000
χ564-444-44-4-400004400-4-400000000000000000000000000-222-2-222-20000000000000000
χ574-444-44-4-40000-4-40044000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ584-444-44-4-40000-4-4004400000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ594-44-44-44-400004i−4i00−4i4i0000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ604-44-44-44-400004i−4i00−4i4i000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ614-44-44-44-40000−4i4i004i−4i0000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ624-44-44-44-40000−4i4i004i−4i000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ634-4-44-4-4444-4-4400000000004-4-44000000000000000000000000000000000000000000
χ644-4-44-4-4444-4-440000000000-444-4000000000000000000000000000000000000000000
χ654-4-44-4-444-444-40000000000000000004-4000000000000000000000000000000000000
χ664-4-44-4-444-444-4000000000000000000-44000000000000000000000000000000000000
χ674-4-4-444-44-44-44000000004-40000-440000000000000000000000000000000000000000
χ684-4-4-444-44-44-4400000000-4400004-40000000000000000000000000000000000000000

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