Finite Group Databasebeta

← Group #306675

Character table — Group #306675

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111
χ51111111111111111111111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-1-1-11-1-1-11111-1-1-1-111-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-111-1-11111-1
χ91111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-111-1-11
χ101111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1111111-1-1-11-1-1-1-111-1-111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-111-11111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111111-1-1-11111-1-1-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-1-111111
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111111-1-1111-1-1-1-1-1-1111
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1111111111-1-1-1
χ17222222222-22-22-22-20000-2-2222222-2-2-2-20000-2-2000000000000000200000000000
χ18222222222-22-22-22-20000-2-22222-2-222220000-2-2000000000000000-200000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-222-2-222000022000000000000000-200000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-2-2-222-2-2000022000000000000000200000000000
χ2122222222-22-22-22-222222-2-20000000000-2-22200-2-20000220000-200000000000000
χ2222222222-22-22-22-222222-2-20000000000-2-2-2-200220000-2-20000200000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000000000222200220000-2-20000-200000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000000000022-2-200-2-20000220000200000000000000
χ2522-22-2-2-22020-20-20222-2-200i2i2−i2−i2000000002-2i2−i200i2i2−i2−i22-2i2i2−i2−i20000000000i2−i2000
χ2622-22-2-2-22020-20-20222-2-200i2i2−i2−i200000000-22i2−i200i2i2−i2−i2-22−i2−i2i2i20000000000−i2i2000
χ2722-22-2-2-22020-20-20222-2-200−i2−i2i2i2000000002-2−i2i200−i2−i2i2i22-2−i2−i2i2i20000000000−i2i2000
χ2822-22-2-2-22020-20-20222-2-200−i2−i2i2i200000000-22−i2i200−i2−i2i2i2-22i2i2−i2−i20000000000i2−i2000
χ2922-22-2-2-22020-20-202-2-22200i2i2−i2−i2000000002-2i2−i200−i2−i2i2i2-22−i2−i2i2i20000000000i2−i2000
χ3022-22-2-2-22020-20-202-2-22200i2i2−i2−i200000000-22i2−i200−i2−i2i2i22-2i2i2−i2−i20000000000−i2i2000
χ3122-22-2-2-22020-20-202-2-22200−i2−i2i2i2000000002-2−i2i200i2i2−i2−i2-22i2i2−i2−i20000000000−i2i2000
χ3222-22-2-2-22020-20-202-2-22200−i2−i2i2i200000000-22−i2i200i2i2−i2−i22-2−i2−i2i2i20000000000i2−i2000
χ332-2-222-22-22-2-222-2-222i−2i2i−2i-2200000000002i−2i00000000000000000000002i−2i00002-20
χ342-2-222-22-22-2-222-2-222i−2i2i−2i-2200000000002i−2i0000000000000000000000−2i2i0000-220
χ352-2-222-22-22-2-222-2-22−2i2i−2i2i-220000000000−2i2i00000000000000000000002i−2i0000-220
χ362-2-222-22-22-2-222-2-22−2i2i−2i2i-220000000000−2i2i0000000000000000000000−2i2i00002-20
χ372-2-222-22-2-222-2-222-20000-2200002-22-200000000002i−2i2i−2i00000002i−2i000000000000
χ382-2-222-22-2-222-2-222-20000-2200002-22-20000000000−2i2i−2i2i0000000−2i2i000000000000
χ392-2-222-22-2-222-2-222-20000-220000-22-2200000000002i−2i2i−2i0000000−2i2i000000000000
χ402-2-222-22-2-222-2-222-20000-220000-22-220000000000−2i2i−2i2i00000002i−2i000000000000
χ412-2-222-22-2-2-222-2-2222i−2i2i−2i2-200002-2-2200−2i2i000000000000000000002i−2i000000000
χ422-2-222-22-2-2-222-2-2222i−2i2i−2i2-20000-222-200−2i2i00000000000000000000−2i2i000000000
χ432-2-222-22-2-2-222-2-222−2i2i−2i2i2-200002-2-22002i−2i00000000000000000000−2i2i000000000
χ442-2-222-22-2-2-222-2-222−2i2i−2i2i2-20000-222-2002i−2i000000000000000000002i−2i000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ4644-44-4-4-440-404040-40000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ4744-44-4-4-440-404040-4000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ4844-4-444-4-44040-40-40000000000000004-4000000000000000000000000000000000
χ4944-4-444-4-44040-40-4000000000000000-44000000000000000000000000000000000
χ5044-4-444-4-4-40-4040400000000000000000000000000000000000000000002i2−2i200000
χ5144-4-444-4-4-40-404040000000000000000000000000000000000000000000−2i22i200000
χ524-444-44-4-404040-40-400000000000000000000000022−22−2222000000000000000000000
χ534-444-44-4-404040-40-4000000000000000000000000−222222−22000000000000000000000
χ544-444-44-4-40-40-404044i−4i−4i4i000000000000000000000000000000000000000000000
χ554-444-44-4-40-40-40404−4i4i4i−4i000000000000000000000000000000000000000000000
χ564-44-44-4-4440-40-40400000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ574-44-44-4-4440-40-4040000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ584-44-44-4-44-404040-400000004i−4i4i−4i000000000000000000000000000000000000000
χ594-44-44-4-44-404040-40000000−4i4i−4i4i000000000000000000000000000000000000000
χ604-4-444-44-444-4-444-4-400004-40000000000000000000000000000000000000000000
χ614-4-4-4-44440000000000000022−22−222200000000000022−220000002-2-22000000000000000
χ624-4-4-4-44440000000000000022−22−2222000000000000−2222000000-222-2000000000000000
χ634-4-4-4-444400000000000000−222222−2200000000000022−22000000-222-2000000000000000
χ644-4-4-4-444400000000000000−222222−22000000000000−22220000002-2-22000000000000000
χ65888-8-8-88-8000000000000000000000000000000000000000000000000000000000

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