Finite Group Databasebeta

← Group #295757

Character table — Group #295757

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444444444444888888888888888844444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-11-1-1-11-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-11-1-1-1-1-11-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-1-11-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-1-1-1-1-111111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1111-1-1-1-111-1-1-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1111-1-11-1-11111-1-1-11
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-111-1-1111-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1111-1-111-1-111-11
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1111-1-1-1-1-1-11111-1-11-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1111-1-1111-1-1-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1111-111-1-111-1-1-11
χ172222222222-2-2-222-222-2-2-2-222-2-20000000000000000002200-2-20200000-20000000000
χ182222222222-2-2-222-222-2-2-2-222-2-2000000000000000000-2-200220-20000020000000000
χ192222222222-2-2-222-2-2-22222-2-2-2-20000000000000000002200220-200000-20000000000
χ202222222222-2-2-222-2-2-22222-2-2-2-2000000000000000000-2-200-2-2020000020000000000
χ2122222222-2-2222-2-222222-2-2-2-2-2-200000000000000002200-2-2002000-20000000000000
χ2222222222-2-2222-2-222222-2-2-2-2-2-20000000000000000-2-2002200-200020000000000000
χ2322222222-2-2222-2-22-2-2-2-22222-2-200000000000000002200-2-200-200020000000000000
χ2422222222-2-2222-2-22-2-2-2-22222-2-20000000000000000-2-20022002000-20000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-2-222000000000000000000000000002-202-200000000000
χ2622222222-2-2-2-2-2-2-2-222-2-222-2-22200000000000000000000000000-220-2200000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-22222000000000000000000000000002-20-2200000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-2222200000000000000000000000000-2202-200000000000
χ2922-22-2-22-22-22-2-22-22000000002-2000000002i2i2i2i−2i−2i−2i−2i2i−2i002i−2i0000000000002-2000000
χ3022-22-2-22-22-22-2-22-22000000002-2000000002i2i2i2i−2i−2i−2i−2i−2i2i00−2i2i000000000000-22000000
χ3122-22-2-22-22-22-2-22-22000000002-200000000−2i−2i−2i−2i2i2i2i2i2i−2i002i−2i000000000000-22000000
χ3222-22-2-22-22-22-2-22-22000000002-200000000−2i−2i−2i−2i2i2i2i2i−2i2i00−2i2i0000000000002-2000000
χ3322-22-2-22-2-222-2-2-22200000000-222i2i2i2i−2i−2i−2i−2i000000002i−2i00−2i2i00000000002-200000000
χ3422-22-2-22-2-222-2-2-22200000000-222i2i2i2i−2i−2i−2i−2i00000000−2i2i002i−2i0000000000-2200000000
χ3522-22-2-22-2-222-2-2-22200000000-22−2i−2i−2i−2i2i2i2i2i000000002i−2i00−2i2i0000000000-2200000000
χ3622-22-2-22-2-222-2-2-22200000000-22−2i−2i−2i−2i2i2i2i2i00000000−2i2i002i−2i00000000002-200000000
χ372-222-2-2-222-2000-220002i−2i2i−2i000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2002i−2i002-2000000000000i2−i22−200
χ382-222-2-2-222-2000-220002i−2i2i−2i000022−2−222−2−2i2i2−i2−i2i2i2−i2−i200−2i2i00-22000000000000−i2i2−2200
χ392-222-2-2-222-2000-220002i−2i2i−2i0000−2−222−2−222−i2−i2i2i2−i2−i2i2i2002i−2i002-2000000000000−i2i2−2200
χ402-222-2-2-222-2000-220002i−2i2i−2i0000−2−222−2−222−i2−i2i2i2−i2−i2i2i200−2i2i00-22000000000000i2−i22−200
χ412-222-2-2-222-2000-22000−2i2i−2i2i000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2002i−2i00-22000000000000i2−i2−2200
χ422-222-2-2-222-2000-22000−2i2i−2i2i000022−2−222−2−2−i2−i2i2i2−i2−i2i2i200−2i2i002-2000000000000−i2i22−200
χ432-222-2-2-222-2000-22000−2i2i−2i2i0000−2−222−2−222i2i2−i2−i2i2i2−i2−i2002i−2i00-22000000000000−i2i22−200
χ442-222-2-2-222-2000-22000−2i2i−2i2i0000−2−222−2−222i2i2−i2−i2i2i2−i2−i200−2i2i002-2000000000000i2−i2−2200
χ45444-44-4-4-4000000004-4000000002-22-22-22-22-22-22-22-200000000000000000000000000
χ46444-44-4-4-4000000004-400000000-22-22-22-22-22-22-22-2200000000000000000000000000
χ47444-44-4-4-400000000-44000000002-22-22-22-2-22-22-22-2200000000000000000000000000
χ48444-44-4-4-400000000-4400000000-22-22-22-222-22-22-22-200000000000000000000000000
χ4944-44-4-44-44-4-4444-4-400000000-44000000000000000000000000000000000000000000
χ5044-44-4-44-4-44-444-44-4000000004-4000000000000000000000000000000000000000000
χ5144-4-4-44-44000000000000004-4002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ5244-4-4-44-44000000000000004-400−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5344-4-4-44-4400000000000000-44002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5444-4-4-44-4400000000000000-4400−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ554-444-4-4-44-440004-40004i−4i−4i4i0000000000000000000000000000000000000000000000
χ564-444-4-4-44-440004-4000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ574-44-4-444-40044-400-4000000000022−22−222222−22−22220000000000000000000000000000000000
χ584-44-4-444-40044-400-40000000000−222222−22−222222−220000000000000000000000000000000000
χ594-44-4-444-400-4-440040000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ604-44-4-444-400-4-44004000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ614-4-4444-4-444000-4-400000000000000000002222−22−22−22−22222200000000000000000000000000
χ624-4-4444-4-444000-4-40000000000000000000−22−2222222222−22−2200000000000000000000000000
χ634-4-4444-4-4-4-400044000000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ644-4-4444-4-4-4-40004400000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ654-4-4-44-444004-4400-400000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000
χ664-4-4-44-444004-4400-40000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000
χ674-4-4-44-44400-44-400400000000000000000022−22−2222−222222−2200000000000000000000000000
χ684-4-4-44-44400-44-4004000000000000000000−222222−2222−22−222200000000000000000000000000

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