Finite Group Databasebeta

← Group #10697227

Character table — Group #10697227

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order12222234444446666666444121212121212121222446666888812121212121224242424242424244412121212888888882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ9222222222-2-2222222222-2-2-2222-2-2-2-2222-2-222220000-2-2-2-2-2-200000000000000000000000000
χ10222222222-2-2222222222-2-2-2222-2-2-2-22-2-222-2-2-2-20000-2-2222200000000000000000000000000
χ112222222-2-222-2-222222222-2-2-2-2-22222-2000000000000-2-20000000000000000002i2i−2i−2i00000000
χ122222222-2-222-2-222222222-2-2-2-2-22222-2000000000000-2-2000000000000000000−2i−2i2i2i00000000
χ132222222-2-2-2-2-2-22222222-222-2-2-2-2-2-2-2-200000000000022000000000000000000000022-2-20000
χ142222222-2-2-2-2-2-22222222-222-2-2-2-2-2-2-2-2000000000000220000000000000000000000-2-2220000
χ15222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ16222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111-2-21111000000000000
χ17222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-1-2-21111000000000000
χ18222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-111111111111122-1-1-1-1000000000000
χ19222222-122-2-222-1-1-1-1-1-1-1-2-2-2-1-1-11111-122-2-2-1-1-1-10000111111−i3−i3−i3−i3i3i3i3i300−i3−i3i3i3000000000000
χ20222222-122-2-222-1-1-1-1-1-1-1-2-2-2-1-1-11111-122-2-2-1-1-1-10000111111i3i3i3i3−i3−i3−i3−i300i3i3−i3−i3000000000000
χ21222222-122-2-222-1-1-1-1-1-1-1-2-2-2-1-1-11111-1-2-2221111000011-1-1-1-1−i3−i3−i3−i3i3i3i3i300i3i3−i3−i3000000000000
χ22222222-122-2-222-1-1-1-1-1-1-1-2-2-2-1-1-11111-1-2-2221111000011-1-1-1-1i3i3i3i3−i3−i3−i3−i300−i3−i3i3i3000000000000
χ232222-2-222-2222-2-2-2-2-2222-22-22-2-222-2-220000000022-2-22-2000022-2-222-2-2000000000000000000
χ242222-2-222-2222-2-2-2-2-2222-22-22-2-222-2-2200000000-2-2222-20000-2-222-2-222000000000000000000
χ252222-2-222-2-2-22-2-2-2-2-22222-222-2-2-2-2222000000000000-220000000000002-22-22-2000000000000
χ262222-2-222-2-2-22-2-2-2-2-22222-222-2-2-2-2222000000000000-22000000000000-22-22-22000000000000
χ272222-2-22-2222-22-2-2-2-2222-2-22-22222-2-2-2000000000000-22000000000000000000000000002-200
χ282222-2-22-2222-22-2-2-2-2222-2-22-22222-2-2-2000000000000-2200000000000000000000000000-2200
χ292222-2-22-22-2-2-22-2-2-2-222222-2-222-2-222-20000000000002-200000000000000000000000000002-2
χ302222-2-22-22-2-2-22-2-2-2-222222-2-222-2-222-20000000000002-20000000000000000000000000000-22
χ312222-2-2-12-2222-21111-1-1-1-22-2-111-1-111-10000−i3−i3i3i322-2-2-11−i3−i3i3i3-1-111-1-11100−i3i3i3−i3000000000000
χ322222-2-2-12-2222-21111-1-1-1-22-2-111-1-111-10000−i3−i3i3i3-2-222-11−i3−i3i3i311-1-111-1-100i3−i3−i3i3000000000000
χ332222-2-2-12-2222-21111-1-1-1-22-2-111-1-111-10000i3i3−i3−i322-2-2-11i3i3−i3−i3-1-111-1-11100i3−i3−i3i3000000000000
χ342222-2-2-12-2222-21111-1-1-1-22-2-111-1-111-10000i3i3−i3−i3-2-222-11i3i3−i3−i311-1-111-1-100−i3i3i3−i3000000000000
χ352222-2-2-12-2-2-22-21111-1-1-12-22-11111-1-1-10000−i3−i3i3i300001-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i32-2-11-11000000000000
χ362222-2-2-12-2-2-22-21111-1-1-12-22-11111-1-1-10000−i3−i3i3i300001-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-221-11-1000000000000
χ372222-2-2-12-2-2-22-21111-1-1-12-22-11111-1-1-10000i3i3−i3−i300001-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-221-11-1000000000000
χ382222-2-2-12-2-2-22-21111-1-1-12-22-11111-1-1-10000i3i3−i3−i300001-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i32-2-11-11000000000000
χ392-22-22-222-200-2222-2-22-2-200022-20000-22-2002-22-2000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ402-22-22-222-200-2222-2-22-2-200022-20000-22-2002-22-2000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ412-22-22-222-200-2222-2-22-2-200022-20000-2-2200-22-22000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ422-22-22-222-200-2222-2-22-2-200022-20000-2-2200-22-22000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ432-22-22-22-22002-222-2-22-2-2000-2-2200002002i−2i00000000002i−2i2i−2i000000000000002−2−22−i2i2i2−i20000
χ442-22-22-22-22002-222-2-22-2-2000-2-2200002002i−2i00000000002i−2i2i−2i00000000000000−222−2i2−i2−i2i20000
χ452-22-22-22-22002-222-2-22-2-2000-2-220000200−2i2i0000000000−2i2i−2i2i000000000000002−2−22i2−i2−i2i20000
χ462-22-22-22-22002-222-2-22-2-2000-2-220000200−2i2i0000000000−2i2i−2i2i00000000000000−222−2−i2i2i2−i20000
χ47444444-2-4-444-4-4-2-2-2-2-2-2-24-4-4222-2-2-2-2200000000000022000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-2-2-2-2-2-2-2-44422222222000000000000-2-2000000000000000000000000000000
χ494444-4-4-2-4444-442222-2-2-2-4-442-2-2-2-22220000000000002-2000000000000000000000000000000
χ504444-4-4-2-44-4-4-442222-2-2-244-42-2-222-2-22000000000000-22000000000000000000000000000000
χ514-44-44-4-24-400-44-2-222-222000-2-22000024-400-22-22000000000000000000000000000000000000
χ524-44-44-4-24-400-44-2-222-222000-2-2200002-44002-22-2000000000000000000000000000000000000
χ534-44-44-4-2-44004-4-2-222-22200022-20000-2004i−4i0000000000−2i2i−2i2i00000000000000000000000000
χ544-44-44-4-2-44004-4-2-222-22200022-20000-200−4i4i00000000002i−2i2i−2i00000000000000000000000000
χ554-44-4-4444400-4-4-4-4444-4-40004-440000-400000000000000000000000000000000000000000000
χ564-44-4-444-4-40044-4-4444-4-4000-44-40000400000000000000000000000000000000000000000000
χ574-44-4-44-24400-4-422-2-2-222000-22-2000020000−2i32i32i3−2i3000000000000000000000000000000000000
χ584-44-4-44-24400-4-422-2-2-222000-22-20000200002i3−2i3−2i32i3000000000000000000000000000000000000
χ594-44-4-44-2-4-4004422-2-2-2220002-220000-20000000000000023−23−232300000000000000000000000000
χ604-44-4-44-2-4-4004422-2-2-2220002-220000-200000000000000−232323−2300000000000000000000000000
χ614-4-44004004-4000000-4-440000004-4000000000000022−220000000022−220022−22000000000000000000
χ624-4-44004004-4000000-4-440000004-40000000000000−222200000000−222200−2222000000000000000000
χ634-4-4400400-44000000-4-44000000-440000000000022−220000000022−220022−2200000000000000000000
χ644-4-4400400-44000000-4-44000000-4400000000000−222200000000−222200−222200000000000000000000
χ654-4-4400-2004-400−2i32i3−2i32i322-2000000-22−2i32i30000000000022−22000000i6−i6−22−i6i6−22000000000000000000
χ664-4-4400-2004-400−2i32i3−2i32i322-2000000-22−2i32i300000000000−2222000000−i6i62−2i6−i62−2000000000000000000
χ674-4-4400-2004-4002i3−2i32i3−2i322-2000000-222i3−2i30000000000022−22000000−i6i6−22i6−i6−22000000000000000000
χ684-4-4400-2004-4002i3−2i32i3−2i322-2000000-222i3−2i300000000000−2222000000i6−i62−2−i6i62−2000000000000000000
χ694-4-4400-200-4400−2i32i3−2i32i322-20000002-22i3−2i300000000022−2200000000−22i6−i6−22−i6i6000000000000000000
χ704-4-4400-200-4400−2i32i3−2i32i322-20000002-22i3−2i3000000000−2222000000002−2−i6i62−2i6−i6000000000000000000
χ714-4-4400-200-44002i3−2i32i3−2i322-20000002-2−2i32i300000000022−2200000000−22−i6i6−22i6−i6000000000000000000
χ724-4-4400-200-44002i3−2i32i3−2i322-20000002-2−2i32i3000000000−2222000000002−2i6−i62−2−i6i6000000000000000000
χ7388-8-80080000000000-88-80000000000000000000000000000000000000000000000000000000
χ7488-8-800-4000000−4i34i34i3−4i34-440000000000000000000000000000000000000000000000000000000
χ7588-8-800-40000004i3−4i3−4i34i34-440000000000000000000000000000000000000000000000000000000

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