Finite Group Databasebeta

← Group #135613

Character table — Group #135613

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222222244444444444448888888888888888888888888816161616161632323232
order122222444444888822444448888882444448888161616161616161616161616161616164444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1111-1-1111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ61111111111111111-1-1111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ71111111111111111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ81111111111111111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1
χ91111111-1-1-1-11111111-1-11-1-111-1-1-1-1-11111111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-1i−ii−i
χ101111111-1-1-1-11111111-1-11-1-111-1-1-1-1-11111111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1−ii−ii
χ111111111-1-1-1-11111111-1-11-1-111-1-1-1-1-11-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111−ii−ii
χ121111111-1-1-1-11111111-1-11-1-111-1-1-1-1-11-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111i−ii−i
χ131111111-1-1-1-111111-1-1-1-111111-1-1-1-11-11111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111i−i−ii
χ141111111-1-1-1-111111-1-1-1-111111-1-1-1-11-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111−iii−i
χ151111111-1-1-1-111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1−iii−i
χ161111111-1-1-1-111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1i−i−ii
χ17222222222222-2-2-2-22222222-2-2-2-2-2-2220000-2-2-2-200000000000000000000000000
χ18222222222222-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000
χ192222222-2-2-2-22-2-2-2-222-2-22-2-2-2-22222-220000-2-22200000000000000000000000000
χ202222222-2-2-2-22-2-2-2-2-2-2-2-2222-2-222222-2000022-2-200000000000000000000000000
χ21222222-22222-2000022-2-2-222000000-2-20000000022−2−222−2−222−2−222−2−20000000000
χ22222222-22222-2000022-2-2-222000000-2-200000000−2−222−2−222−2−222−2−2220000000000
χ23222222-22222-20000-2-2-2-2-2-2-2000000220000000022−2−222−2−2−2−222−2−2220000000000
χ24222222-22222-20000-2-2-2-2-2-2-20000002200000000−2−222−2−22222−2−222−2−20000000000
χ25222222-2-2-2-2-2-200002222-2-2-20000002-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000
χ26222222-2-2-2-2-2-200002222-2-2-20000002-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000
χ27222222-2-2-2-2-2-20000-2-222-222000000-2200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000
χ28222222-2-2-2-2-2-20000-2-222-222000000-2200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000
χ292222-2-2222-2-222222002-2-200-2-222-2-200000000000000000000000000002i−2i2i−2i0000
χ302222-2-2222-2-222222002-2-200-2-222-2-20000000000000000000000000000−2i2i−2i2i0000
χ312222-2-2222-2-22-2-2-2-2002-2-20022-2-222002i2i−2i−2i000000000000000000002i−2i00000000
χ322222-2-2222-2-22-2-2-2-2002-2-20022-2-22200−2i−2i2i2i00000000000000000000−2i2i00000000
χ332222-2-22-2-2222222200-22-200-2-2-2-22200000000000000000000000000002i−2i−2i2i0000
χ342222-2-22-2-2222222200-22-200-2-2-2-2220000000000000000000000000000−2i2i2i−2i0000
χ352222-2-22-2-2222-2-2-2-200-22-2002222-2-2002i2i−2i−2i00000000000000000000−2i2i00000000
χ362222-2-22-2-2222-2-2-2-200-22-2002222-2-200−2i−2i2i2i000000000000000000002i−2i00000000
χ3722-2-22-202i−2i2i−2i022−2−22-20002i−2i2−2i2−i2i2−i20000002−2i2−i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ30000000000
χ3822-2-22-202i−2i2i−2i022−2−22-20002i−2i2−2i2−i2i2−i20000002−2i2−i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000000000
χ3922-2-22-202i−2i2i−2i022−2−2-22000−2i2i2−2i2−i2i2−i2000000−22−i2i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000000000
χ4022-2-22-202i−2i2i−2i022−2−2-22000−2i2i2−2i2−i2i2−i2000000−22−i2i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ30000000000
χ4122-2-22-202i−2i2i−2i0−2−2222-20002i−2i−22−i2i2−i2i2000000−22−i2i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000000000
χ4222-2-22-202i−2i2i−2i0−2−2222-20002i−2i−22−i2i2−i2i2000000−22−i2i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ70000000000
χ4322-2-22-202i−2i2i−2i0−2−222-22000−2i2i−22−i2i2−i2i20000002−2i2−i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ70000000000
χ4422-2-22-202i−2i2i−2i0−2−222-22000−2i2i−22−i2i2−i2i20000002−2i2−i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000000000
χ4522-2-22-20−2i2i−2i2i022−2−22-2000−2i2i2−2−i2i2−i2i20000002−2−i2i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ70000000000
χ4622-2-22-20−2i2i−2i2i022−2−22-2000−2i2i2−2−i2i2−i2i20000002−2−i2i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000000000
χ4722-2-22-20−2i2i−2i2i022−2−2-220002i−2i2−2−i2i2−i2i2000000−22i2−i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000000000
χ4822-2-22-20−2i2i−2i2i022−2−2-220002i−2i2−2−i2i2−i2i2000000−22i2−i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ70000000000
χ4922-2-22-20−2i2i−2i2i0−2−2222-2000−2i2i−22i2−i2i2−i2000000−22i2−i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000000000
χ5022-2-22-20−2i2i−2i2i0−2−2222-2000−2i2i−22i2−i2i2−i2000000−22i2−i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ30000000000
χ5122-2-22-20−2i2i−2i2i0−2−222-220002i−2i−22i2−i2i2−i20000002−2−i2i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ30000000000
χ5222-2-22-20−2i2i−2i2i0−2−222-220002i−2i−22i2−i2i2−i20000002−2−i2i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000000000
χ534444-4-4-444-4-4-4000000-44400000000000000000000000000000000000000000000
χ544444-4-4-4-4-444-40000004-4400000000000000000000000000000000000000000000
χ5544-4-4-4404i−4i−4i4i02222−22−220000000−22222i2−2i2−2i22i2000000000000000000000000000000000000
χ5644-4-4-4404i−4i−4i4i0−22−222222000000022−22−2i22i22i2−2i2000000000000000000000000000000000000
χ5744-4-4-440−4i4i4i−4i02222−22−220000000−2222−2i22i22i2−2i2000000000000000000000000000000000000
χ5844-4-4-440−4i4i4i−4i0−22−222222000000022−222i2−2i2−2i22i2000000000000000000000000000000000000
χ594-4-440040000-44i−4i4i−4i0000000000000002+2i−2−2i2−2i−2+2i000000000000000000000000000000
χ604-4-440040000-44i−4i4i−4i000000000000000−2−2i2+2i−2+2i2−2i000000000000000000000000000000
χ614-4-440040000-4−4i4i−4i4i0000000000000002−2i−2+2i2+2i−2−2i000000000000000000000000000000
χ624-4-440040000-4−4i4i−4i4i000000000000000−2+2i2−2i−2−2i2+2i000000000000000000000000000000
χ638-88-8000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000000
χ648-88-800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000000
χ658-8-8800-80000800000000000000000000000000000000000000000000000000000

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