Finite Group Databasebeta

← Group #138619

Character table — Group #138619

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222244444488884448888888888882244444488888888888881616161616161616161616164488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ91111-1-1-111-1-1-1111111-1-1-1-1ii−i−iii−i−i-111-1-1-1-1111iiii−i−i−i−iii−i−iiiii−i−i−i−i11-1-11-1i−i
χ101111-1-1-111-1-1-1111111-1-1-1-1ii−i−iii−i−i-111-1-1-1-1111iiii−i−i−i−iii−i−i−i−i−i−iiiii-1-111-11−ii
χ111111-1-1-111-1-1-1111111-1-1-1-1ii−i−iii−i−i-1-1-11111-1-11−i−i−i−iiiiiii−i−iiiii−i−i−i−i11-1-1-11−ii
χ121111-1-1-111-1-1-1111111-1-1-1-1ii−i−iii−i−i-1-1-11111-1-11−i−i−i−iiiiiii−i−i−i−i−i−iiiii-1-1111-1i−i
χ131111-1-1-111-1-1-1111111-1-1-1-1−i−iii−i−iii-111-1-1-1-1111−i−i−i−iiiii−i−iiiiiii−i−i−i−i-1-111-11i−i
χ141111-1-1-111-1-1-1111111-1-1-1-1−i−iii−i−iii-111-1-1-1-1111−i−i−i−iiiii−i−iii−i−i−i−iiiii11-1-11-1−ii
χ151111-1-1-111-1-1-1111111-1-1-1-1−i−iii−i−iii-1-1-11111-1-11iiii−i−i−i−i−i−iiiiiii−i−i−i−i-1-1111-1−ii
χ161111-1-1-111-1-1-1111111-1-1-1-1−i−iii−i−iii-1-1-11111-1-11iiii−i−i−i−i−i−iii−i−i−i−iiiii11-1-1-11i−i
χ17222222222222-2-2-2-2222-2-2-222222222-200000000-200000000-2-2-2-20000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-200000000-20000000022220000000000000000
χ19222222222-22-22222-2-2-22-2-20000000022222-2-2-2-2-20000000000000000000000000000
χ20222222222-22-22222-2-2-22-2-2000000002-2-2-2-22222-20000000000000000000000000000
χ21222222222-22-2-2-2-2-2-2-2-2-22200000000-20000000022i2i−2i−2i2i2i−2i−2i00000000000000000000
χ22222222222-22-2-2-2-2-2-2-2-2-22200000000-2000000002−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ23222222-2-2-2-2-2-20000-2220002i2i−2i−2i−2i−2i2i2i0000000000000000000000i2i2−i2−i2i2i2−i2−i22−22−20000
χ24222222-2-2-2-2-2-20000-2220002i2i−2i−2i−2i−2i2i2i0000000000000000000000−i2−i2i2i2−i2−i2i2i2−22−220000
χ25222222-2-2-2-2-2-20000-222000−2i−2i2i2i2i2i−2i−2i0000000000000000000000i2i2−i2−i2i2i2−i2−i2−22−220000
χ26222222-2-2-2-2-2-20000-222000−2i−2i2i2i2i2i−2i−2i0000000000000000000000−i2−i2i2i2−i2−i2i2i22−22−20000
χ272222-2-22-2-22220000-22-20002222-2-2-2-2000000000000000000000022−2−2−2−2222−2−220000
χ282222-2-22-2-22220000-22-20002222-2-2-2-20000000000000000000000−2−22222−2−2−222−20000
χ292222-2-22-2-22220000-22-2000-2-2-2-22222000000000000000000000022−2−2−2−222−222−20000
χ302222-2-22-2-22220000-22-2000-2-2-2-222220000000000000000000000−2−22222−2−22−2−220000
χ312222-2-2-2222-222222-2-22-22200000000-222-2-222-2-2-20000000000000000000000000000
χ322222-2-2-2222-222222-2-22-22200000000-2-2-222-2-222-20000000000000000000000000000
χ332222-2-2-2222-22-2-2-2-2-2-222-2-200000000200000000222-2-2-2-22200000000000000000000
χ342222-2-2-2222-22-2-2-2-2-2-222-2-2000000002000000002-2-22222-2-200000000000000000000
χ352222-2-2-222-2-2-2-2-2-2-222-22222i2i−2i−2i2i2i−2i−2i200000000-200000000−2i−2i2i2i0000000000000000
χ362222-2-2-222-2-2-2-2-2-2-222-2222−2i−2i2i2i−2i−2i2i2i200000000-2000000002i2i−2i−2i0000000000000000
χ3722-2-22-222-20-2022-2-20002002−22−22−22−2-22-22-2000002−22−22−22−22−22−20000000000000000
χ3822-2-22-222-20-2022-2-20002002−22−22−22−2-2-22-2200000−22−22−22−222−22−20000000000000000
χ3922-2-22-222-20-2022-2-2000200−22−22−22−22-22-22-200000−22−22−22−22−22−220000000000000000
χ4022-2-22-222-20-2022-2-2000200−22−22−22−22-2-22-22000002−22−22−22−2−22−220000000000000000
χ4122-2-22-222-20-20-2-222000-2002−22−22−22−2200002i−2i2i−2i0i2−i2−i2i2i2−i2−i2i2−22−220000000000000000
χ4222-2-22-222-20-20-2-222000-2002−22−22−22−220000−2i2i−2i2i0−i2i2i2−i2−i2i2i2−i2−22−220000000000000000
χ4322-2-22-222-20-20-2-222000-200−22−22−22−22200002i−2i2i−2i0−i2i2i2−i2−i2i2i2−i22−22−20000000000000000
χ4422-2-22-222-20-20-2-222000-200−22−22−22−2220000−2i2i−2i2i0i2−i2−i2i2i2−i2−i2i22−22−20000000000000000
χ4522-2-2-22-22-202022-2-2000-200i2−i2−i2i2i2−i2−i2i222-2-2200000i2−i2i2−i2−i2i2−i2i2i2−i2−i2i20000000000000000
χ4622-2-2-22-22-202022-2-2000-200i2−i2−i2i2i2−i2−i2i22-222-200000−i2i2−i2i2i2−i2i2−i2i2−i2−i2i20000000000000000
χ4722-2-2-22-22-202022-2-2000-200−i2i2i2−i2−i2i2i2−i222-2-2200000−i2i2−i2i2i2−i2i2−i2−i2i2i2−i20000000000000000
χ4822-2-2-22-22-202022-2-2000-200−i2i2i2−i2−i2i2i2−i22-222-200000i2−i2i2−i2−i2i2−i2i2−i2i2i2−i20000000000000000
χ4922-2-2-22-22-2020-2-222000200i2−i2−i2i2i2−i2−i2i2-200002i−2i−2i2i02−2−22−222−2−i2i2i2−i20000000000000000
χ5022-2-2-22-22-2020-2-222000200i2−i2−i2i2i2−i2−i2i2-20000−2i2i2i−2i0−222−22−2−22−i2i2i2−i20000000000000000
χ5122-2-2-22-22-2020-2-222000200−i2i2i2−i2−i2i2i2−i2-200002i−2i−2i2i0−222−22−2−22i2−i2−i2i20000000000000000
χ5222-2-2-22-22-2020-2-222000200−i2i2i2−i2−i2i2i2−i2-20000−2i2i2i−2i02−2−22−222−2i2−i2−i2i20000000000000000
χ53444444-4-4-44-4400004-4-40000000000000000000000000000000000000000000000000
χ544444-4-44-4-4-44-400004-440000000000000000000000000000000000000000000000000
χ5544-4-44-4-4-4404000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ5644-4-44-4-4-440400000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ5744-4-4-444-440-40000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ5844-4-4-444-440-400000000000−2222−222222−2222−2200000000000000000000000000000000000000
χ594-44-40000040-422−2222−22000022−22000000000000000000000000000000ζ+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+ζ700000000
χ604-44-40000040-422−2222−22000022−22000000000000000000000000000000−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−ζ700000000
χ614-44-40000040-4−2222−22220000−2222000000000000000000000000000000ζ−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+ζ700000000
χ624-44-40000040-4−2222−22220000−2222000000000000000000000000000000−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−ζ700000000
χ634-44-400000-40422−2222−220000−2222000000000000000000000000000000ζ+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+ζ700000000
χ644-44-400000-40422−2222−220000−2222000000000000000000000000000000−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−ζ700000000
χ654-44-400000-404−2222−2222000022−22000000000000000000000000000000ζ−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+ζ700000000
χ664-44-400000-404−2222−2222000022−22000000000000000000000000000000−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−ζ700000000
χ678-8-880000000042−42−42420000000000000000000000000000000000000000000000000000
χ688-8-8800000000−424242−420000000000000000000000000000000000000000000000000000

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