Finite Group Databasebeta

← Group #112425

Character table — Group #112425

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222222444444444444442444448888888888888888888888882224444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-111111-1-1-1-1
χ9111111-1-111111-1-1-1-1-1-1-1-11-11-111-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ10111111-1-111111-1-1-1-1-1-1-1-11-11-111-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ11111111-1-111111-1-1-1-1-1-1-1-11-11-111-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-11-1-11ii−i−i−i−iii
χ12111111-1-111111-1-1-1-1-1-1-1-11-11-111-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111-111-1−i−iiiii−i−i
χ13111111-1-111111-1-1-1-1-1-1-1-11-11-111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ14111111-1-111111-1-1-1-1-1-1-1-11-11-111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ15111111-1-111111-1-1-1-1-1-1-1-11-11-111-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-11-1-11−i−iiiii−i−i
χ16111111-1-111111-1-1-1-1-1-1-1-11-11-111-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111-111-1ii−i−i−i−iii
χ17222222222222-2-2-2-2-2-2-2-2-2-22-22-2-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2-2-22-22-2-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ1922222222-2-2-2-22-2-22222-2-2222-2-2-2-2000000000000000000000000002-2-200200000000
χ2022222222-2-2-2-22-2-22222-2-2222-2-2-2-200000000000000000000000000-22200-200000000
χ2122222222-2-2-2-2-222-2-2-2-222-22-2-222-20000000000000000000000000000000000002i−2i2i−2i
χ2222222222-2-2-2-2-222-2-2-2-222-22-2-222-2000000000000000000000000000000000000−2i2i−2i2i
χ23222222-2-22222-222222222-2-2-2-2-2-2-222-2-2-2-22200000000000000000000000000000000
χ24222222-2-22222-222222222-2-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ25222222-2-2-2-2-2-2222-2-2-2-2222-222-2-22000000000000000000000000002-2200-200000000
χ26222222-2-2-2-2-2-2222-2-2-2-2222-222-2-2200000000000000000000000000-22-200200000000
χ27222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-222220000000000000000000000000000000000002-2-22
χ28222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-22222000000000000000000000000000000000000-222-2
χ292222-2-22222-2-222222-2-2-2-22-2-2-22-220000000022-2-222-2-2000000000000000000000000
χ302222-2-22222-2-222222-2-2-2-22-2-2-22-2200000000-2-222-2-222000000000000000000000000
χ312222-2-22222-2-2-2-2-2-2-22222-2-22-2-222000000000000000022-2-222-2-20000000000000000
χ322222-2-22222-2-2-2-2-2-2-22222-2-22-2-2220000000000000000-2-222-2-2220000000000000000
χ332222-2-222-2-2222-2-222-2-2222-2-22-22-20000000000000000000000002-20002-2000000000
χ342222-2-222-2-2222-2-222-2-2222-2-22-22-2000000000000000000000000-22000-22000000000
χ352222-2-222-2-222-222-2-222-2-2-2-2222-2-2000000000000000000000000000000002i−2i2i−2i0000
χ362222-2-222-2-222-222-2-222-2-2-2-2222-2-200000000000000000000000000000000−2i2i−2i2i0000
χ372222-2-2-2-222-2-22-2-2-2-2222222-222-2-20000000022-2-2-2-222000000000000000000000000
χ382222-2-2-2-222-2-22-2-2-2-2222222-222-2-200000000-2-22222-2-2000000000000000000000000
χ392222-2-2-2-222-2-2-22222-2-2-2-2-2222-22-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402222-2-2-2-222-2-2-22222-2-2-2-2-2222-22-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ412222-2-2-2-2-2-222222-2-222-2-222-2-2-2220000000000000000000000002-2000-22000000000
χ422222-2-2-2-2-2-222222-2-222-2-222-2-2-222000000000000000000000000-220002-2000000000
χ432222-2-2-2-2-2-222-2-2-222-2-222-222-22-22000000000000000000000000000000002-2-220000
χ442222-2-2-2-2-2-222-2-2-222-2-222-222-22-2200000000000000000000000000000000-222-20000
χ4522-2-22-2002-22-202i−2i2i−2i2i−2i2i−2i0000000002ζ3−2ζ32ζ−2ζ002−22−2i2−i2i2−i21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4622-2-22-2002-22-202i−2i2i−2i2i−2i2i−2i0000000002ζ3−2ζ32ζ−2ζ00−22−22−i2i2−i2i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4722-2-22-2002-22-202i−2i2i−2i2i−2i2i−2i000000000−2ζ32ζ3−2ζ2ζ002−22−2i2−i2i2−i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4822-2-22-2002-22-202i−2i2i−2i2i−2i2i−2i000000000−2ζ32ζ3−2ζ2ζ00−22−22−i2i2−i2i21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4922-2-22-2002-22-20−2i2i−2i2i−2i2i−2i2i0000000002ζ−2ζ2ζ3−2ζ3002−22−2−i2i2−i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ5022-2-22-2002-22-20−2i2i−2i2i−2i2i−2i2i0000000002ζ−2ζ2ζ3−2ζ300−22−22i2−i2i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ5122-2-22-2002-22-20−2i2i−2i2i−2i2i−2i2i000000000−2ζ2ζ−2ζ32ζ3002−22−2−i2i2−i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ5222-2-22-2002-22-20−2i2i−2i2i−2i2i−2i2i000000000−2ζ2ζ−2ζ32ζ300−22−22i2−i2i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ5322-2-2-22002-2-2202i−2i2i−2i−2i2i−2i2i00000002ζ−2ζ00002ζ3−2ζ32−2−22i2−i2−i2i21+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ5422-2-2-22002-2-2202i−2i2i−2i−2i2i−2i2i00000002ζ−2ζ00002ζ3−2ζ3−222−2−i2i2i2−i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ5522-2-2-22002-2-2202i−2i2i−2i−2i2i−2i2i0000000−2ζ2ζ0000−2ζ32ζ32−2−22i2−i2−i2i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ5622-2-2-22002-2-2202i−2i2i−2i−2i2i−2i2i0000000−2ζ2ζ0000−2ζ32ζ3−222−2−i2i2i2−i21+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ5722-2-2-22002-2-220−2i2i−2i2i2i−2i2i−2i00000002ζ3−2ζ300002ζ−2ζ2−2−22−i2i2i2−i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ5822-2-2-22002-2-220−2i2i−2i2i2i−2i2i−2i00000002ζ3−2ζ300002ζ−2ζ−222−2i2−i2−i2i21−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ5922-2-2-22002-2-220−2i2i−2i2i2i−2i2i−2i0000000−2ζ32ζ30000−2ζ2ζ2−2−22−i2i2i2−i21−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ6022-2-2-22002-2-220−2i2i−2i2i2i−2i2i−2i0000000−2ζ32ζ30000−2ζ2ζ−222−2i2−i2−i2i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ6144-4-44-400-44-4404i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000
χ6244-4-44-400-44-440−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000
χ6344-4-4-4400-444-404i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000
χ6444-4-4-4400-444-40−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000
χ658-88-800000000800000000-80000000000000000000000000000000000000000000000
χ668-88-800000000-80000000080000000000000000000000000000000000000000000000
χ678-8-88008-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8800-88000000000000000000000000000000000000000000000000000000000000

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