Finite Group Databasebeta

← Group #10591581

Character table — Group #10591581

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222222222444444444466666666888888888899991212121212121212121212121818242424243636
order12223344666666344666121212128888888812121212121212121212444444442424242424242424441212121244
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1
χ3111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ5111111111111111-1-1111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1
χ6111111111111111-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111
χ7111111111111111-1-11111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ911-1-1111-1-1-1-11-1111-1-1-111-1-1111-1-1ii−i−i1-11-11-111-1-1ii−i−i1-1i−i11-1-1ii−i−ii−ii−i1-1i−i
χ1011-1-1111-1-1-1-11-1111-1-1-111-1-1111-1-1−i−iii1-11-11-111-1-1−i−iii1-1−ii11-1-1−i−iii−ii−ii1-1−ii
χ1111-1-1111-1-1-1-11-1111-1-1-111-1-11-1-111ii−i−i1-11-11-111-1-1−i−iii-11i−i-1-111ii−i−i−iii−i-11−ii
χ1211-1-1111-1-1-1-11-1111-1-1-111-1-11-1-111−i−iii1-11-11-111-1-1ii−i−i-11−ii-1-111−i−iiii−i−ii-11i−i
χ1311-1-1111-1-1-1-11-111-11-1-111-1-1111-1-1ii−i−i-11-111-1-1-111ii−i−i-11−ii11-1-1ii−i−ii−i−ii-11−ii
χ1411-1-1111-1-1-1-11-111-11-1-111-1-1111-1-1−i−iii-11-111-1-1-111−i−iii-11i−i11-1-1−i−iii−iii−i-11i−i
χ1511-1-1111-1-1-1-11-111-11-1-111-1-11-1-111ii−i−i-11-111-1-1-111−i−iii1-1−ii-1-111ii−i−i−ii−ii1-1i−i
χ1611-1-1111-1-1-1-11-111-11-1-111-1-11-1-111−i−iii-11-111-1-1-111ii−i−i1-1i−i-1-111−i−iiii−ii−i1-1−ii
χ17222222-2-2222222200222-2-2-2-2000000000000-2-200002222000000000000-2-2000000
χ18222222-2-2222222200222-2-2-2-2000000000000-2-20000-2-2-2-200000000000022000000
χ1922222-12222-1-1-12-122-1-1-1-12-1200002222-1-122-1-1-1-1-1-1000000220000-1-1-1-100-1-10000
χ2022222-12222-1-1-12-122-1-1-1-12-120000-2-2-2-2-1-122-1-1-1-1-1-1000000-2-20000111100110000
χ2122222-12222-1-1-12-1-2-2-1-1-1-12-120000222211-2-2-1-11111000000-2-20000-1-1-1-100110000
χ2222222-12222-1-1-12-1-2-2-1-1-1-12-120000-2-2-2-211-2-2-1-11111000000220000111100-1-10000
χ232222-1222-1-1222-1-122-1-1-12-12-12222000022-1-1-1-1-1-1-1-100002200-1-1-1-100000000-1-100
χ242222-1222-1-1222-1-122-1-1-12-12-1-2-2-2-2000022-1-1-1-1-1-1-1-10000-2-2001111000000001100
χ252222-1222-1-1222-1-1-2-2-1-1-12-12-122220000-2-211-1-111110000-2-200-1-1-1-1000000001100
χ262222-1222-1-1222-1-1-2-2-1-1-12-12-1-2-2-2-20000-2-211-1-1111100002200111100000000-1-100
χ2722-2-222-22-2-2-22-22200-2-22-222-2000000000000-2200002i2i−2i−2i000000000000−2i2i000000
χ2822-2-222-22-2-2-22-22200-2-22-222-2000000000000-220000−2i−2i2i2i0000000000002i−2i000000
χ2922-2-22-12-2-2-21-112-12-211-1-1-21200002i2i−2i−2i-112-2-11-1-1110000002i−2i0000−i−iii00−ii0000
χ3022-2-22-12-2-2-21-112-12-211-1-1-2120000−2i−2i2i2i-112-2-11-1-111000000−2i2i0000ii−i−i00i−i0000
χ3122-2-22-12-2-2-21-112-1-2211-1-1-21200002i2i−2i−2i1-1-22-1111-1-1000000−2i2i0000−i−iii00i−i0000
χ3222-2-22-12-2-2-21-112-1-2211-1-1-2120000−2i−2i2i2i1-1-22-1111-1-10000002i−2i0000ii−i−i00−ii0000
χ3322-2-2-122-211-22-2-1-12-211-121-2-122-2-200002-2-11-11-1-11100002-200-1-11100000000-1100
χ3422-2-2-122-211-22-2-1-12-211-121-2-1-2-22200002-2-11-11-1-1110000-220011-1-1000000001-100
χ3522-2-2-122-211-22-2-1-1-2211-121-2-122-2-20000-221-1-1111-1-10000-2200-1-111000000001-100
χ3622-2-2-122-211-22-2-1-1-2211-121-2-1-2-2220000-221-1-1111-1-100002-20011-1-100000000-1100
χ372-22-222002-22-2-2-22002-2-200002−22−22−22−200000000002-22-200002−22−22−22−200000000
χ382-22-222002-22-2-2-22002-2-200002−22−2−22−220000000000-22-2200002−22−2−22−2200000000
χ392-22-222002-22-2-2-22002-2-20000−22−222−22−20000000000-22-220000−22−222−22−200000000
χ402-22-222002-22-2-2-22002-2-20000−22−22−22−2200000000002-22-20000−22−22−22−2200000000
χ412-2-222200-22-2-22-2200-22-200002−2−22i2−i2−i2i200000000002i−2i−2i2i00002−2−22i2−i2−i2i200000000
χ422-2-222200-22-2-22-2200-22-200002−2−22−i2i2i2−i20000000000−2i2i2i−2i00002−2−22−i2i2i2−i200000000
χ432-2-222200-22-2-22-2200-22-20000−222−2i2−i2−i2i20000000000−2i2i2i−2i0000−222−2i2−i2−i2i200000000
χ442-2-222200-22-2-22-2200-22-20000−222−2−i2i2i2−i200000000002i−2i−2i2i0000−222−2−i2i2i2−i200000000
χ4544444-2-4-444-2-2-24-200-2-2-22-42-4000000000000220000000000000000000000000000
χ464444-24-4-4-2-2444-2-200-2-2-2-42-42000000000000220000000000000000000000000000
χ474444-2-244-2-2-2-2-2-2144111-2-2-2-200000000-2-2-2-2111111000000000000000000000000
χ484444-2-244-2-2-2-2-2-21-4-4111-2-2-2-200000000222211-1-1-1-1000000000000000000000000
χ494444-2-2-4-4-2-2-2-2-2-21001112222000000000000-1-13-33-3000000000000000000000000
χ504444-2-2-4-4-2-2-2-2-2-21001112222000000000000-1-1-33-33000000000000000000000000
χ5144-4-44-2-44-4-42-224-20022-224-2-40000000000002-20000000000000000000000000000
χ5244-4-4-24-4422-44-4-2-20022-2-4-2420000000000002-20000000000000000000000000000
χ5344-4-4-2-24-4222-22-214-4-1-11-222-200000000-22-221-111-1-1000000000000000000000000
χ5444-4-4-2-24-4222-22-21-44-1-11-222-2000000002-22-21-1-1-111000000000000000000000000
χ5544-4-4-2-2-44222-22-2100-1-112-2-22000000000000-113-3-33000000000000000000000000
χ5644-4-4-2-2-44222-22-2100-1-112-2-22000000000000-11-333-3000000000000000000000000
χ574-44-44-2004-4-222-4-200-2220000000022−2222−220000000000000000000000−22−2200000000
χ584-44-44-2004-4-222-4-200-22200000000−2222−222200000000000000000000002−22−200000000
χ594-44-4-2400-224-4-42-200-222000022−2222−220000000000000000000000−22−22000000000000
χ604-44-4-2400-224-4-42-200-2220000−2222−222200000000000000000000002−22−2000000000000
χ614-4-444-200-4422-2-4-2002-22000000002i2−2i2−2i22i20000000000000000000000−i2i2i2−i200000000
χ624-4-444-200-4422-2-4-2002-2200000000−2i22i22i2−2i20000000000000000000000i2−i2−i2i200000000
χ634-4-44-24002-2-4-442-2002-22000022−22−22220000000000000000000000−222−2000000000000
χ644-4-44-24002-2-4-442-2002-220000−222222−2200000000000000000000002−2−22000000000000
χ658-88-8-4-400-44-44442002-2-20000000000000000000000000000000000000000000000
χ668-8-88-4-4004-444-44200-22-20000000000000000000000000000000000000000000000

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