Finite Group Databasebeta

← Group #141557

Character table — Group #141557

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222444444444444444888888888888888888888816161616323232323232
order12222244888822444444488888824888888888888888888884444448888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-1-1-1-1-1-1-111-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1ii−i−i
χ6111111111111111-1-1-1-1-1-1-1-1-1-111-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111−i−iii
χ7111111111111111-1-1-1-1-1-1-1-1-1-111-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1−i−iii
χ8111111111111111-1-1-1-1-1-1-1-1-1-111-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111ii−i−i
χ911111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-11-11-1
χ1011111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-11-11-11
χ1111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-11-11
χ1211111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-111-11-1
χ1311111111-1-1-1-1111-1-1-1-1-1-11111-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-11i−i−ii
χ1411111111-1-1-1-1111-1-1-1-1-1-11111-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1111-1−iii−i
χ1511111111-1-1-1-1111-1-1-1-1-1-11111-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11−iii−i
χ1611111111-1-1-1-1111-1-1-1-1-1-11111-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1i−i−ii
χ17222222222222-2-222222-2-2222222-2-2-2-2-2-200000000000000000000000000
χ18222222222222-2-22-2-2-2-222-2-2-2-2222-2-2-22200000000000000000000000000
χ1922222222-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000
χ2022222222-2-2-2-2-2-22-2-2-2-2222222-2-22-222-2-200000000000000000000000000
χ21222222-2-2000022-222-2-222000000-2-20000000022-2-2000022-2-20000000000
χ22222222-2-2000022-222-2-222000000-2-200000000-2-2220000-2-2220000000000
χ23222222-2-2000022-2-2-222-2-20000002-2000000002i2i−2i−2i0000−2i−2i2i2i0000000000
χ24222222-2-2000022-2-2-222-2-20000002-200000000−2i−2i2i2i00002i2i−2i−2i0000000000
χ25222222-2-20000-2-2-222-2-2-2-20000002200002i2i−2i−2i00002i2i−2i−2i00000000000000
χ26222222-2-20000-2-2-222-2-2-2-2000000220000−2i−2i2i2i0000−2i−2i2i2i00000000000000
χ27222222-2-20000-2-2-2-2-22222000000-22000022-2-20000-2-22200000000000000
χ28222222-2-20000-2-2-2-2-22222000000-220000-2-222000022-2-200000000000000
χ292-22-22-200i2i2−i2−i22-202i−2i002i−2i22−2−2i2−i200i2−i22−21+i−1−i1+i−1−i002ζ3−2ζ31−i−1+i1−i−1+i002ζ−2ζ0000000000
χ302-22-22-200i2i2−i2−i22-202i−2i002i−2i22−2−2i2−i200i2−i22−2−1−i1+i−1−i1+i00−2ζ32ζ3−1+i1−i−1+i1−i00−2ζ2ζ0000000000
χ312-22-22-200i2i2−i2−i22-20−2i2i00−2i2i−2−222i2−i200i2−i2−221−i−1+i1−i−1+i002ζ−2ζ1+i−1−i1+i−1−i002ζ3−2ζ30000000000
χ322-22-22-200i2i2−i2−i22-20−2i2i00−2i2i−2−222i2−i200i2−i2−22−1+i1−i−1+i1−i00−2ζ2ζ−1−i1+i−1−i1+i00−2ζ32ζ30000000000
χ332-22-22-200i2i2−i2−i2-2202i−2i00−2i2i22−2−2i2−i200−i2i2−221−i−1+i−1+i1−i2ζ−2ζ00−1−i1+i1+i−1−i2ζ3−2ζ3000000000000
χ342-22-22-200i2i2−i2−i2-2202i−2i00−2i2i22−2−2i2−i200−i2i2−22−1+i1−i1−i−1+i−2ζ2ζ001+i−1−i−1−i1+i−2ζ32ζ3000000000000
χ352-22-22-200i2i2−i2−i2-220−2i2i002i−2i−2−222i2−i200−i2i22−21+i−1−i−1−i1+i2ζ3−2ζ300−1+i1−i1−i−1+i2ζ−2ζ000000000000
χ362-22-22-200i2i2−i2−i2-220−2i2i002i−2i−2−222i2−i200−i2i22−2−1−i1+i1+i−1−i−2ζ32ζ3001−i−1+i−1+i1−i−2ζ2ζ000000000000
χ372-22-22-200−i2−i2i2i22-202i−2i002i−2i−2−222−i2i200−i2i2−221+i−1−i1+i−1−i00−2ζ32ζ31−i−1+i1−i−1+i00−2ζ2ζ0000000000
χ382-22-22-200−i2−i2i2i22-202i−2i002i−2i−2−222−i2i200−i2i2−22−1−i1+i−1−i1+i002ζ3−2ζ3−1+i1−i−1+i1−i002ζ−2ζ0000000000
χ392-22-22-200−i2−i2i2i22-20−2i2i00−2i2i22−2−2−i2i200−i2i22−21−i−1+i1−i−1+i00−2ζ2ζ1+i−1−i1+i−1−i00−2ζ32ζ30000000000
χ402-22-22-200−i2−i2i2i22-20−2i2i00−2i2i22−2−2−i2i200−i2i22−2−1+i1−i−1+i1−i002ζ−2ζ−1−i1+i−1−i1+i002ζ3−2ζ30000000000
χ412-22-22-200−i2−i2i2i2-2202i−2i00−2i2i−2−222−i2i200i2−i22−21−i−1+i−1+i1−i−2ζ2ζ00−1−i1+i1+i−1−i−2ζ32ζ3000000000000
χ422-22-22-200−i2−i2i2i2-2202i−2i00−2i2i−2−222−i2i200i2−i22−2−1+i1−i1−i−1+i2ζ−2ζ001+i−1−i−1−i1+i2ζ3−2ζ3000000000000
χ432-22-22-200−i2−i2i2i2-220−2i2i002i−2i22−2−2−i2i200i2−i2−221+i−1−i−1−i1+i−2ζ32ζ300−1+i1−i1−i−1+i−2ζ2ζ000000000000
χ442-22-22-200−i2−i2i2i2-220−2i2i002i−2i22−2−2−i2i200i2−i2−22−1−i1+i1+i−1−i2ζ3−2ζ3001−i−1+i−1+i1−i2ζ−2ζ000000000000
χ454444-4-444444400-40000000000-4-400000000000000000000000000000000
χ464444-4-444-4-4-4-400-400000000004400000000000000000000000000000000
χ474444-4-4-4-400000040000004i−4i4i−4i0000000000000000000000000000000000
χ484444-4-4-4-40000004000000−4i4i−4i4i0000000000000000000000000000000000
χ4944-4-400-444-44-400000000000000000000000000000000000002i−2i2i−2i000000
χ5044-4-400-444-44-40000000000000000000000000000000000000−2i2i−2i2i000000
χ5144-4-400-44-44-4400000000000000000000000000000000000002i−2i−2i2i000000
χ5244-4-400-44-44-440000000000000000000000000000000000000−2i2i2i−2i000000
χ534-44-4-44002i22i2−2i2−2i2000004-4002i2−2i2−2i22i2−2i22i200000000000000000000000000000000
χ544-44-4-44002i22i2−2i2−2i200000-4400−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ554-44-4-4400−2i2−2i22i22i2000004-400−2i22i22i2−2i22i2−2i200000000000000000000000000000000
χ564-44-4-4400−2i2−2i22i22i200000-44002i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ5788-8-8008-8000000000000000000000000000000000000000000000000000
χ588-8-8800004i2−4i2−4i24i200000000000000000000000000000000000000000000000
χ598-8-880000−4i24i24i2−4i200000000000000000000000000000000000000000000000

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