Finite Group Databasebeta

← Group #138488

Character table — Group #138488

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11112222444444444448888888888888161616161616161616161616161632323232
order12224444244448888882444816161616161616168888888888161616164488
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ81111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ9111111-1-11-1-1-1111-1-1-1-111-1-11iiii−i−i−i−i1-1ii−i−iii−i−iii−i−i1-11-1
χ10111111-1-11-1-1-1111-1-1-1-111-1-11iiii−i−i−i−i1-1−i−iii−i−iiiii−i−i-11-11
χ11111111-1-11-1-1-1111-1-1-1-111-1-11−i−i−i−iiiii1-1ii−i−iii−i−i−i−iii-11-11
χ12111111-1-11-1-1-1111-1-1-1-111-1-11−i−i−i−iiiii1-1−i−iii−i−iii−i−iii1-11-1
χ13111111-1-11-1-1-1111-1-1-1-1-1-1111iiii−i−i−i−i-11ii−i−i−i−iii−i−iii1-1-11
χ14111111-1-11-1-1-1111-1-1-1-1-1-1111iiii−i−i−i−i-11−i−iiiii−i−i−i−iii-111-1
χ15111111-1-11-1-1-1111-1-1-1-1-1-1111−i−i−i−iiiii-11ii−i−i−i−iiiii−i−i-111-1
χ16111111-1-11-1-1-1111-1-1-1-1-1-1111−i−i−i−iiiii-11−i−iiiii−i−iii−i−i1-1-11
χ172222222222222-2-2-2-2-2-22222-200000000-2-20000000000000000
χ182222222222222-2-2-2-2-2-2-2-2-2-2-200000000220000000000000000
χ1922222222-22-2-2-22222-2-20000-2000000000000002-22-200000000
χ2022222222-22-2-2-22222-2-20000-200000000000000-22-2200000000
χ2122222222-22-2-2-2-2-2-2-2220000200000000002-22-2000000000000
χ2222222222-22-2-2-2-2-2-2-222000020000000000-22-22000000000000
χ23222222-2-22-2-2-22-2-2222222-2-2-200000000-220000000000000000
χ24222222-2-22-2-2-22-2-22222-2-222-2000000002-20000000000000000
χ25222222-2-2-2-222-222-2-2220000-2000000000000002i−2i−2i2i00000000
χ26222222-2-2-2-222-222-2-2220000-200000000000000−2i2i2i−2i00000000
χ27222222-2-2-2-222-2-2-222-2-20000200000000002i−2i−2i2i000000000000
χ28222222-2-2-2-222-2-2-222-2-2000020000000000−2i2i2i−2i000000000000
χ292222-2-222-2-22-220000002-22-2022−2−222−2−200000000002−22−20000
χ302222-2-222-2-22-220000002-22-20−2−222−2−2220000000000−22−220000
χ312222-2-222-2-22-22000000-22-22022−2−222−2−20000000000−22−220000
χ322222-2-222-2-22-22000000-22-220−2−222−2−22200000000002−22−20000
χ332222-2-2-2-2-22-2220000002-2-220i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i20000
χ342222-2-2-2-2-22-2220000002-2-220−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i20000
χ352222-2-2-2-2-22-222000000-222-20i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i20000
χ362222-2-2-2-2-22-222000000-222-20−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i20000
χ374444-4-4444-4-44-40000000000000000000000000000000000000
χ384444-4-4-4-4444-4-40000000000000000000000000000000000000
χ394-44-4004i−4i0000022−222i2−2i20000000ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5+ζ7ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5−ζ7ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5+ζ7ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5−ζ7000000000000000000
χ404-44-4004i−4i0000022−222i2−2i20000000−ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5−ζ7−ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5+ζ7−ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5−ζ7−ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5+ζ7000000000000000000
χ414-44-4004i−4i00000−2222−2i22i20000000ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5−ζ7−ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5−ζ7−ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5+ζ7ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5+ζ7000000000000000000
χ424-44-4004i−4i00000−2222−2i22i20000000−ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5+ζ7ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5+ζ7ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5−ζ7−ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5−ζ7000000000000000000
χ434-44-400−4i4i0000022−22−2i22i20000000ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5+ζ7−ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5+ζ7ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5+ζ7−ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5+ζ7000000000000000000
χ444-44-400−4i4i0000022−22−2i22i20000000−ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5−ζ7ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5−ζ7−ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5−ζ7ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5−ζ7000000000000000000
χ454-44-400−4i4i00000−22222i2−2i20000000ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5−ζ7ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5+ζ7−ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5+ζ7−ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5−ζ7000000000000000000
χ464-44-400−4i4i00000−22222i2−2i20000000−ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5+ζ7−ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5−ζ7ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5−ζ7ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5+ζ7000000000000000000
χ4788-8-88-800000000000000000000000000000000000000000000
χ4888-8-8-8800000000000000000000000000000000000000000000
χ498-8-8800000000000004i2−4i20000000000000000000000000000000
χ508-8-880000000000000−4i24i20000000000000000000000000000000

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