Finite Group Databasebeta

← Group #306607

Character table — Group #306607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888222244444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-11-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111
χ51111111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1111-1-1-1-111-1
χ61111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11
χ71111111111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-111-1-11111-1
χ911111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-111-1-11
χ1011111111111111111-1-1-1-111111111111-1-1-1-111-1-1-1-111111111-1-11-1-1-1-1-111-1-111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1111-1-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-111-111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-11111111-1-1-1-1-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-111-1-1-1-1-111111
χ1511111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111111-1-11-1-1-1-1-1-1111
χ1611111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1111-1-1-1111111-1-1-1
χ17222222222-22-22-22-2-20000-2222222-2-2-2-20000000000-2-2000000002000000000000
χ18222222222-22-22-22-2-20000-22222-2-222220000000000-2-200000000-2000000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-22222-2-200000000002200000000-2000000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-2-2-2-2-222000000000022000000002000000000000
χ2122222222-22-22-22-22-22222-20000000000-2-222-2-200000022000000000-2000000000
χ2222222222-22-22-22-22-22222-20000000000-2-2-2-222000000-2-20000000002000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000000000222222000000-2-2000000000-2000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000000000022-2-2-2-2000000220000000002000000000
χ252-22-222-2-22-2-222-2-22-22i2i−2i−2i200000000002i−2i00000000000000000000002i−2i00002-20
χ262-22-222-2-22-2-222-2-22-22i2i−2i−2i200000000002i−2i0000000000000000000000−2i2i0000-220
χ272-22-222-2-22-2-222-2-22-2−2i−2i2i2i20000000000−2i2i00000000000000000000002i−2i0000-220
χ282-22-222-2-22-2-222-2-22-2−2i−2i2i2i20000000000−2i2i0000000000000000000000−2i2i00002-20
χ292-22-222-2-2-222-2-222-2-20000200002-2002-20000002i2i−2i−2i000000000002i−2i0000000000
χ302-22-222-2-2-222-2-222-2-20000200002-2002-2000000−2i−2i2i2i00000000000−2i2i0000000000
χ312-22-222-2-2-222-2-222-2-2000020000-2200-220000002i2i−2i−2i00000000000−2i2i0000000000
χ322-22-222-2-2-222-2-222-2-2000020000-2200-22000000−2i−2i2i2i000000000002i−2i0000000000
χ332-22-222-2-2-2-222-2-22222i2i−2i−2i-200002-200-22−2i2i00000000000000002i−2i0000000000000
χ342-22-222-2-2-2-222-2-22222i2i−2i−2i-20000-22002-2−2i2i0000000000000000−2i2i0000000000000
χ352-22-222-2-2-2-222-2-2222−2i−2i2i2i-200002-200-222i−2i0000000000000000−2i2i0000000000000
χ362-22-222-2-2-2-222-2-2222−2i−2i2i2i-20000-22002-22i−2i00000000000000002i−2i0000000000000
χ372-2-222-22-202020-20-202-22-2022−2−2000000002i−2i002−22−22−22i−2ii2i2−i2−i20000000000i2−i2000
χ382-2-222-22-202020-20-202-22-2022−2−200000000−2i2i002−22−22−2−2i2i−i2−i2i2i20000000000−i2i2000
χ392-2-222-22-202020-20-202-22-20−2−222000000002i−2i00−22−22−222i−2i−i2−i2i2i20000000000−i2i2000
χ402-2-222-22-202020-20-202-22-20−2−22200000000−2i2i00−22−22−22−2i2ii2i2−i2−i20000000000i2−i2000
χ412-2-222-22-202020-20-20-22-22022−2−2000000002i−2i00−22−222−2−2i2i−i2−i2i2i20000000000i2−i2000
χ422-2-222-22-202020-20-20-22-22022−2−200000000−2i2i00−22−222−22i−2ii2i2−i2−i20000000000−i2i2000
χ432-2-222-22-202020-20-20-22-220−2−222000000002i−2i002−22−2−22−2i2ii2i2−i2−i20000000000−i2i2000
χ442-2-222-22-202020-20-20-22-220−2−22200000000−2i2i002−22−2−222i−2i−i2−i2i2i20000000000i2−i2000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ4644-44-44-4-44040-40-4000000000000000000000000000000022−2222−22000000000000000
χ4744-44-44-4-44040-40-40000000000000000000000000000000−2222−2222000000000000000
χ4844-44-44-4-4-40-4040400000004i−4i4i−4i000000000000000000000000000000000000000
χ4944-44-44-4-4-40-404040000000−4i4i−4i4i000000000000000000000000000000000000000
χ5044-4-44-4-44040-40-40400000000000000000000002i2−2i2−2i22i200000000000000000000000
χ5144-4-44-4-44040-40-4040000000000000000000000−2i22i22i2−2i200000000000000000000000
χ5244-4-44-4-440-404040-404i−4i−4i4i00000000000000000000000000000000000000000000
χ5344-4-44-4-440-404040-40−4i4i4i−4i00000000000000000000000000000000000000000000
χ544-444-4-4-44000000000000002i2−2i2−2i22i2000000000022−22000000002i−2i−2i2i000000000000000
χ554-444-4-4-44000000000000002i2−2i2−2i22i20000000000−222200000000−2i2i2i−2i000000000000000
χ564-444-4-4-4400000000000000−2i22i22i2−2i2000000000022−2200000000−2i2i2i−2i000000000000000
χ574-444-4-4-4400000000000000−2i22i22i2−2i20000000000−2222000000002i−2i−2i2i000000000000000
χ584-44-444-4-444-4-444-4-440000-40000000000000000000000000000000000000000000
χ594-4-444-44-40-40-404040000002222−22−220000000000000000−2222000000000000000000000
χ604-4-444-44-40-40-40404000000−22−222222000000000000000022−22000000000000000000000
χ614-4-4-4-444440-40-40400000000000004-400000000000000000000000000000000000
χ624-4-4-4-444440-40-4040000000000000-4400000000000000000000000000000000000
χ634-4-4-4-4444-404040-4000000000000000000000000000000000000000000022−2200000
χ644-4-4-4-4444-404040-40000000000000000000000000000000000000000000−222200000
χ65888-8-8-88-8000000000000000000000000000000000000000000000000000000000

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