Finite Group Databasebeta

← Group #10696718

Character table — Group #10696718

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order12223444444666244466121212121212121288881212242424242424242444441212121212121212888888884488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-111
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111
χ922222222-2-22222-2-22-2-2-222-2-222-2-20000-2200000000000000000000000000002-200
χ1022222222-2-22222-2-22-2-2-222-2-222-2-20000-220000000000000000000000000000-2200
χ112222222-222-2222-2-2-22-2-222-2-2-2-22222-2-22-22222-2-2-2-2000000000000000000000000
χ122222222-222-2222-2-2-22-2-222-2-2-2-222-2-2222-2-2-2-2-22222000000000000000000000000
χ132222222-2-2-2-222222-2-2222222-2-2-2-20000-2-2000000000000000000002i2i−2i−2i00000000
χ142222222-2-2-2-222222-2-2222222-2-2-2-20000-2-200000000000000000000−2i−2i2i2i00000000
χ1522222-2-22222222-22-2-2-2-2-2-22222220000-2-200000000002-2-2-2000022000000000000
χ1622222-2-22222222-22-2-2-2-2-2-22222220000-2-20000000000-22220000-2-2000000000000
χ1722222-2-22-2-222222-2-2222-2-2-2-222-2-200002-20000000000000000000000000000002-2
χ1822222-2-22-2-222222-2-2222-2-2-2-222-2-200002-2000000000000000000000000000000-22
χ1922222-2-2-222-22222-22-222-2-2-2-2-2-2220000-22000000002-2000022-2-200000000000000
χ2022222-2-2-222-22222-22-222-2-2-2-2-2-2220000-2200000000-220000-2-22200000000000000
χ2122222-2-2-2-2-2-2222-2222-2-2-2-222-2-2-2-200002200000000000000000000000022-2-20000
χ2222222-2-2-2-2-2-2222-2222-2-2-2-222-2-2-2-2000022000000000000000000000000-2-2220000
χ232222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ242222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ252222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-211-1-1-1-111000000000000
χ262222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-222-1-11111-1-1000000000000
χ272222-122-222-2-1-1-1-2-2-2211-1-11111-1-122-2-2-11-1-1-1-111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ282222-122-222-2-1-1-1-2-2-2211-1-11111-1-122-2-2-11-1-1-1-111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ292222-122-222-2-1-1-1-2-2-2211-1-11111-1-1-2-222-111111-1-1-1-10000−i3i3i3−i3i3−i3−i3i3000000000000
χ302222-122-222-2-1-1-1-2-2-2211-1-11111-1-1-2-222-111111-1-1-1-10000i3−i3−i3i3−i3i3i3−i3000000000000
χ312222-1-2-22222-1-1-1-22-2-21111-1-1-1-1-1-1000011−i3−i3i3i3−i3−i3i3i3002-211−i3i3i3−i3-1-1000000000000
χ322222-1-2-22222-1-1-1-22-2-21111-1-1-1-1-1-1000011−i3−i3i3i3−i3−i3i3i300-22-1-1i3−i3−i3i311000000000000
χ332222-1-2-22222-1-1-1-22-2-21111-1-1-1-1-1-1000011i3i3−i3−i3i3i3−i3−i3002-211i3−i3−i3i3-1-1000000000000
χ342222-1-2-22222-1-1-1-22-2-21111-1-1-1-1-1-1000011i3i3−i3−i3i3i3−i3−i300-22-1-1−i3i3i3−i311000000000000
χ352222-1-2-2-222-2-1-1-12-22-2-1-1111111-1-100001-1−i3−i3i3i3i3i3−i3−i32-200i3−i3-1-111−i3i3000000000000
χ362222-1-2-2-222-2-1-1-12-22-2-1-1111111-1-100001-1−i3−i3i3i3i3i3−i3−i3-2200−i3i311-1-1i3−i3000000000000
χ372222-1-2-2-222-2-1-1-12-22-2-1-1111111-1-100001-1i3i3−i3−i3−i3−i3i3i32-200−i3i3-1-111i3−i3000000000000
χ382222-1-2-2-222-2-1-1-12-22-2-1-1111111-1-100001-1i3i3−i3−i3−i3−i3i3i3-2200i3−i311-1-1−i3i3000000000000
χ394444-2444-4-44-2-2-2-4-44-422-2-222-2-22200002-200000000000000000000000000000000
χ404444-244-4-4-4-4-2-2-244-4-4-2-2-2-2-2-2222200002200000000000000000000000000000000
χ414444-2-4-44-4-44-2-2-24-4-44-2-22222-2-2220000-2200000000000000000000000000000000
χ424444-2-4-4-4-4-4-4-2-2-2-44442222-2-222220000-2-200000000000000000000000000000000
χ4344-4-440004-40-4-440000000000004-40000000000000000000000000000002i−2i2i−2i0000
χ4444-4-440004-40-4-440000000000004-4000000000000000000000000000000−2i2i−2i2i0000
χ4544-4-44000-440-4-44000000000000-440000000000000000000000000000002i−2i−2i2i0000
χ4644-4-44000-440-4-44000000000000-44000000000000000000000000000000−2i2i2i−2i0000
χ474-44-444-400004-4-40000004-40000000022−2200000022−2222−22000000000000000000000000
χ484-44-444-400004-4-40000004-400000000−2222000000−2222−2222000000000000000000000000
χ494-44-44-4400004-4-4000000-4400000022−22000022−2222−220000000000000000000000000000
χ504-44-44-4400004-4-4000000-44000000−22220000−2222−22220000000000000000000000000000
χ514-44-4-24-40000-2220000−2i32i3-22−2i32i300000022−2200i6−i6−i6i6−22−22000000000000000000000000
χ524-44-4-24-40000-2220000−2i32i3-22−2i32i3000000−222200−i6i6i6−i62−22−2000000000000000000000000
χ534-44-4-24-40000-22200002i3−2i3-222i3−2i300000022−2200−i6i6i6−i6−22−22000000000000000000000000
χ544-44-4-24-40000-22200002i3−2i3-222i3−2i3000000−222200i6−i6−i6i62−22−2000000000000000000000000
χ554-44-4-2-440000-2220000−2i32i32-22i3−2i3000022−220000−22−22−i6i6i6−i6000000000000000000000000
χ564-44-4-2-440000-2220000−2i32i32-22i3−2i30000−222200002−22−2i6−i6−i6i6000000000000000000000000
χ574-44-4-2-440000-22200002i3−2i32-2−2i32i3000022−220000−22−22i6−i6−i6i6000000000000000000000000
χ584-44-4-2-440000-22200002i3−2i32-2−2i32i30000−222200002−22−2−i6i6i6−i6000000000000000000000000
χ594-4-44400400-4-44-400000000004-400000000000000000000000000002-22-200000000
χ604-4-44400400-4-44-400000000004-40000000000000000000000000000-22-2200000000
χ614-4-44400-4004-44-40000000000-4400000000000000000000000000002i−2i−2i2i00000000
χ624-4-44400-4004-44-40000000000-440000000000000000000000000000−2i2i2i−2i00000000
χ6388-8-8-40008-8044-4000000000000-4400000000000000000000000000000000000000
χ6488-8-8-4000-88044-40000000000004-400000000000000000000000000000000000000
χ658-8-88-400800-84-440000000000-440000000000000000000000000000000000000000
χ668-8-88-400-80084-4400000000004-40000000000000000000000000000000000000000

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