Finite Group Databasebeta

← Group #93201

Character table — Group #93201

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1111222248888888888881616161616161616161616161616161616161616163232
order122244442444488888888444441616161616161616161616161616161688
χ111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111-1-1-1-1-1-1-1-111111iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111111-1-1-1-1-1-1-1-111111−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111111-1-1-1-1-1-1-1-1-1-11-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111111-1-1-1-1-1-1-1-1-1-11-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ91111-1-1-1-111-1-1-1i−iii−i−ii−i1-111-1ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6i−i
χ101111-1-1-1-111-1-1-1i−iii−i−ii−i1-111-1−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6i−i
χ111111-1-1-1-111-1-1-1i−iii−i−ii−i-111-11ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ii
χ121111-1-1-1-111-1-1-1i−iii−i−ii−i-111-11−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ii
χ131111-1-1-1-111-1-1-1−ii−i−iii−ii1-111-1ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ii
χ141111-1-1-1-111-1-1-1−ii−i−iii−ii1-111-1−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ii
χ151111-1-1-1-111-1-1-1−ii−i−iii−ii-111-11ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2i−i
χ161111-1-1-1-111-1-1-1−ii−i−iii−ii-111-11−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2i−i
χ172222222222-2-2222-2-2-2-22200-200000000000000000000
χ182222222222-2-22-2-22222-2-200-200000000000000000000
χ192222-2-2-2-22222-22i−2i−2i−2i2i2i2i−2i00-200000000000000000000
χ202222-2-2-2-22222-2−2i2i2i2i−2i−2i−2i2i00-200000000000000000000
χ21444444444-400-40000000000000000000000000000000
χ2244444-4-44-4000000000000220-2-2000000000000000000
χ2344444-4-44-4000000000000-2-2022000000000000000000
χ244444-444-4-40000000000002-20-22000000000000000000
χ254444-444-4-4000000000000-2202-2000000000000000000
χ264444-4-4-4-44-40040000000000000000000000000000000
χ274-44-4400-400000220000-2-200000000000002−22−22−22−200
χ284-44-4400-400000220000-2-20000000000000−22−22−22−2200
χ294-44-4400-400000-2-20000220000000000000i2−i2i2−i2−i2i2−i2i200
χ304-44-4400-400000-2-20000220000000000000−i2i2−i2i2i2−i2i2−i200
χ314-44-4-4004000002i−2i0000−2i2i00000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00
χ324-44-4-4004000002i−2i0000−2i2i0000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00
χ334-44-4-400400000−2i2i00002i−2i00000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00
χ344-44-4-400400000−2i2i00002i−2i0000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00
χ354-4-4404i−4i000000002ζ2−2ζ22ζ6−2ζ60000000ζ3+ζ7−ζ3−ζ7ζ3−ζ7−ζ3+ζ7ζ−ζ5−ζ+ζ5ζ+ζ5−ζ−ζ50000000000
χ364-4-4404i−4i000000002ζ2−2ζ22ζ6−2ζ60000000−ζ3−ζ7ζ3+ζ7−ζ3+ζ7ζ3−ζ7−ζ+ζ5ζ−ζ5−ζ−ζ5ζ+ζ50000000000
χ374-4-4404i−4i00000000−2ζ22ζ2−2ζ62ζ60000000ζ3−ζ7−ζ3+ζ7−ζ3−ζ7ζ3+ζ7ζ+ζ5−ζ−ζ5−ζ+ζ5ζ−ζ50000000000
χ384-4-4404i−4i00000000−2ζ22ζ2−2ζ62ζ60000000−ζ3+ζ7ζ3−ζ7ζ3+ζ7−ζ3−ζ7−ζ−ζ5ζ+ζ5ζ−ζ5−ζ+ζ50000000000
χ394-4-440−4i4i000000002ζ6−2ζ62ζ2−2ζ20000000ζ−ζ5−ζ+ζ5ζ+ζ5−ζ−ζ5−ζ3−ζ7ζ3+ζ7−ζ3+ζ7ζ3−ζ70000000000
χ404-4-440−4i4i000000002ζ6−2ζ62ζ2−2ζ20000000−ζ+ζ5ζ−ζ5−ζ−ζ5ζ+ζ5ζ3+ζ7−ζ3−ζ7ζ3−ζ7−ζ3+ζ70000000000
χ414-4-440−4i4i00000000−2ζ62ζ6−2ζ22ζ20000000ζ+ζ5−ζ−ζ5−ζ+ζ5ζ−ζ5−ζ3+ζ7ζ3−ζ7ζ3+ζ7−ζ3−ζ70000000000
χ424-4-440−4i4i00000000−2ζ62ζ6−2ζ22ζ20000000−ζ−ζ5ζ+ζ5ζ−ζ5−ζ+ζ5ζ3−ζ7−ζ3+ζ7−ζ3−ζ7ζ3+ζ70000000000
χ4388-8-80000004-400000000000000000000000000000000
χ4488-8-8000000-4400000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.