Finite Group Databasebeta

← Group #311376

Character table — Group #311376

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888224444888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111111-11-1-111-1-11-1
χ911111111111111111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111
χ1011111111111111111-1-1-1-11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111111-1-1-1-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111-1-1-111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-111111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1111-1-1111-1
χ17222222222-22-2-222-2-22222-200000000000022-2-2-2-222-2-2000000000000000000000000
χ18222222222-22-2-222-2-22222-2000000000000-2-2-2-222-2-222000000000000000000000000
χ19222222222-22-2-222-2-2-2-2-2-2-20000000000002222-2-2-2-222000000000000000000000000
χ20222222222-22-2-222-2-2-2-2-2-2-2000000000000-2-2222222-2-2000000000000000000000000
χ2122222222-22-222-2-22-20000-22222-2-2-2-22222000000000000000000000000-2-200000000
χ2222222222-22-222-2-22-20000-22222-2-2-2-2-2-2-2-20000000000000000000000002200000000
χ2322222222-22-222-2-22-20000-2-2-2-2-2222222-2-2000000000000000000000000-2200000000
χ2422222222-22-222-2-22-20000-2-2-2-2-22222-2-2220000000000000000000000002-200000000
χ252222-2-2-2-222-2-2-22-22-2000022i2i−2i−2i2i2i−2i−2i000000000000000000000000002-2002i−2i000000
χ262222-2-2-2-222-2-2-22-22-2000022i2i−2i−2i2i2i−2i−2i00000000000000000000000000-2200−2i2i000000
χ272222-2-2-2-222-2-2-22-22-200002−2i−2i2i2i−2i−2i2i2i000000000000000000000000002-200−2i2i000000
χ282222-2-2-2-222-2-2-22-22-200002−2i−2i2i2i−2i−2i2i2i00000000000000000000000000-22002i−2i000000
χ292222-2-2-2-2-222-2-2-22222i2i−2i−2i-22i2i−2i−2i−2i−2i2i2i0000002i−2i00000022-2-200000000000000000000
χ302222-2-2-2-2-222-2-2-22222i2i−2i−2i-2−2i−2i2i2i2i2i−2i−2i0000002i−2i000000-2-22200000000000000000000
χ312222-2-2-2-2-222-2-2-2222−2i−2i2i2i-22i2i−2i−2i−2i−2i2i2i000000−2i2i000000-2-22200000000000000000000
χ322222-2-2-2-2-222-2-2-2222−2i−2i2i2i-2−2i−2i2i2i2i2i−2i−2i000000−2i2i00000022-2-200000000000000000000
χ332222-2-2-2-2-2-2222-22-2-22i2i−2i−2i200000000000000−2i2i00000000002i2i−2i−2i22-2-2000000000000
χ342222-2-2-2-2-2-2222-22-2-22i2i−2i−2i200000000000000−2i2i0000000000−2i−2i2i2i-2-222000000000000
χ352222-2-2-2-2-2-2222-22-2-2−2i−2i2i2i2000000000000002i−2i00000000002i2i−2i−2i-2-222000000000000
χ362222-2-2-2-2-2-2222-22-2-2−2i−2i2i2i2000000000000002i−2i0000000000−2i−2i2i2i22-2-2000000000000
χ3722-2-222-2-2-202002-2002-22-20i2−i2i2−i2i2−i2i2−i2000000002i−2i002i−2ii2−i2i2−i22−22−22−22−2000000000000
χ3822-2-222-2-2-202002-2002-22-20i2−i2i2−i2i2−i2i2−i200000000−2i2i00−2i2ii2−i2i2−i2−22−22−22−22000000000000
χ3922-2-222-2-2-202002-2002-22-20−i2i2−i2i2−i2i2−i2i2000000002i−2i002i−2i−i2i2−i2i2−22−22−22−22000000000000
χ4022-2-222-2-2-202002-2002-22-20−i2i2−i2i2−i2i2−i2i200000000−2i2i00−2i2i−i2i2−i2i22−22−22−22−2000000000000
χ4122-2-222-2-2-202002-200-22-220i2−i2i2−i2i2−i2i2−i2000000002i−2i00−2i2i−i2i2−i2i22−22−2−22−22000000000000
χ4222-2-222-2-2-202002-200-22-220i2−i2i2−i2i2−i2i2−i200000000−2i2i002i−2i−i2i2−i2i2−22−222−22−2000000000000
χ4322-2-222-2-2-202002-200-22-220−i2i2−i2i2−i2i2−i2i2000000002i−2i00−2i2ii2−i2i2−i2−22−222−22−2000000000000
χ4422-2-222-2-2-202002-200-22-220−i2i2−i2i2−i2i2−i2i200000000−2i2i002i−2ii2−i2i2−i22−22−2−22−22000000000000
χ4522-2-2-2-22220200-2-2002i−2i−2i2i02−2−22−222−200002i−2i00002-200−i2i2i2−i2i2−i2−i2i22−2−22000000000000
χ4622-2-2-2-22220200-2-2002i−2i−2i2i02−2−22−222−20000−2i2i0000-2200−i2i2i2−i2−i2i2i2−i2−222−2000000000000
χ4722-2-2-2-22220200-2-2002i−2i−2i2i0−222−22−2−2200002i−2i00002-200i2−i2−i2i2−i2i2i2−i2−222−2000000000000
χ4822-2-2-2-22220200-2-2002i−2i−2i2i0−222−22−2−220000−2i2i0000-2200i2−i2−i2i2i2−i2−i2i22−2−22000000000000
χ4922-2-2-2-22220200-2-200−2i2i2i−2i02−2−22−222−200002i−2i0000-2200i2−i2−i2i2i2−i2−i2i2−222−2000000000000
χ5022-2-2-2-22220200-2-200−2i2i2i−2i02−2−22−222−20000−2i2i00002-200i2−i2−i2i2−i2i2i2−i22−2−22000000000000
χ5122-2-2-2-22220200-2-200−2i2i2i−2i0−222−22−2−2200002i−2i0000-2200−i2i2i2−i2−i2i2i2−i22−2−22000000000000
χ5222-2-2-2-22220200-2-200−2i2i2i−2i0−222−22−2−220000−2i2i00002-200−i2i2i2−i2i2−i2−i2i2−222−2000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ544444-4-4-4-44-4-4444-4-440000-40000000000000000000000000000000000000000000000
χ5544-4-444-4-440-400-4400000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ5644-4-444-4-440-400-440000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ5744-4-4-4-444-40-40044000000022−22−222222−22−222200000000000000000000000000000000000000
χ5844-4-4-4-444-40-400440000000−222222−22−222222−2200000000000000000000000000000000000000
χ594-44-44-44-40404-400-4000000000000004i−4i000000000000000000000000000000000000
χ604-44-44-44-40404-400-400000000000000−4i4i000000000000000000000000000000000000
χ614-44-44-44-40-40-44004000000000000000000000000000000000000000000000022−220000
χ624-44-44-44-40-40-440040000000000000000000000000000000000000000000000−22220000
χ634-44-4-44-44040-4400-400000000000000004i−4i0000000000000000000000000000000000
χ644-44-4-44-44040-4400-40000000000000000−4i4i0000000000000000000000000000000000
χ654-44-4-44-440-404-400400000000000000000000000000000000000000000000000022−2200
χ664-44-4-44-440-404-4004000000000000000000000000000000000000000000000000−222200
χ678-8-888-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-88-888-8000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).