Finite Group Databasebeta

← Group #13148553

Character table — Group #13148553

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order122234466624121233666666612366666121212121212224444444412121212666121212121244444446612121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-11-1-111-1-1-1-1-1-1-1-1-1-111-1-111
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-11-111-1-11111-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ51111111111-1-11111111111-1-11-1-111111-1-1111111-1-111-1-11111-1-1-1-111-1-111-1-1-11-111111111-1-1-1-111-1-1-1-1
χ61111111111-1-11111111111-1-11-1-111111-1-11111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-11-11-1-1111-1-1-1-1-1-111111111-1-1
χ71111111111-1-11111111111-1-11-1-111111-1-111-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-11-111-1-1-11111-1-11111-1-1-1-111
χ81111111111-1-11111111111-1-11-1-111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-111-1-11-1111-11-1-1-1-1-1-111-1-1-1-1-1-11111
χ911111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-11111-1-111111111111-1-1-1-1-1-1-11-1-1-111111-1-1-1-1-1-111-1-1-11-11
χ1011111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-11-111-11-111-1-1111111-1-1-1-11-1-11
χ1111111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-11-11-1-111-1-11111-1-111-111-1
χ1211111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11-1111-1-1-1-1-111-1-1-1-111111-11-1
χ1311111-1-1111-11-1-111111111-111-1-1111-1-111-1-111111111-1-11111-1-1-11-1-111-1-1-111-1-11111-1-1-1-111-1-1-1-11-11-1
χ1411111-1-1111-11-1-111111111-111-1-1111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-11-1-1111-1-1-111111-1-11111-1-111-1-1-111-1
χ1511111-1-1111-11-1-111111111-111-1-1111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-11-1-1111111-1-1-1-1-111-1-111-1-111111-1-11
χ1611111-1-1111-11-1-111111111-111-1-1111-1-111-1-1-1-1-1-11111-1-11111-1-1-11-1-111-111-1-111-1-1-1-111-1-111-1-111-11-11
χ17222222222222222-1-1-1222-122-122-1-1-12222-1-122000000000000-1-1-1-1-1-1-1-10220200-1-10000000000-1-100-1-1
χ18222222222222222-1-1-1222-122-122-1-1-12222-1-1-2-2000000000000-1-1-1-1-1-1-1-10-2-20-200110000000000110011
χ1922222222222222-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1220000222222-1-1-1-12-1-12-1-1-1-12000000000000-1-1-1-1-1-1000000
χ2022222222222222-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1220000-2-2-2-2-2-211112-1-12-1-1-1-1-2000000000000111111000000
χ212222222222-2-2222-1-1-1222-1-2-2-1-2-2-1-1-122-2-2-1-1220000000000001111-1-11102-20-200-1-10000000000-1-10011
χ222222222222-2-2222-1-1-1222-1-2-2-1-2-2-1-1-122-2-2-1-1-2-20000000000001111-1-1110-2202001100000000001100-1-1
χ232222222222-2-222-1222-1-1-12-2-2-111-1-1-1-1-11122000022-2-2221111-211-2-1-111-200000000000011-1-1-1-1000000
χ242222222222-2-222-1222-1-1-12-2-2-111-1-1-1-1-111220000-2-222-2-2-1-1-1-1-211-2-1-1112000000000000-1-11111000000
χ2522222-2-22222-2-2-22-1-1-1222-12-2-122-1-1-1-2-2-2-21122000000000000-1-1-1111110-220-200-1-1000000000011001-1
χ2622222-2-22222-2-2-22-1-1-1222-12-2-122-1-1-1-2-2-2-211-2-2000000000000-1-1-11111102-20200110000000000-1-100-11
χ2722222-2-22222-2-2-2-1222-1-1-122-2-1-1-1-1-1-11111-2-2000022-2-2-2-211112-1-1-211112000000000000-1-1-1-111000000
χ2822222-2-22222-2-2-2-1222-1-1-122-2-1-1-1-1-1-11111-2-20000-2-22222-1-1-1-12-1-1-21111-20000000000001111-1-1000000
χ2922222-2-2222-22-2-22-1-1-1222-1-22-1-2-2-1-1-1-2-2221122000000000000111-111-1-10-2-20200-1-100000000001100-11
χ3022222-2-2222-22-2-22-1-1-1222-1-22-1-2-2-1-1-1-2-22211-2-2000000000000111-111-1-10220-200110000000000-1-1001-1
χ3122222-2-2222-22-2-2-1222-1-1-12-22-111-1-1-111-1-1-2-200002222-2-2-1-1-1-1-211211-1-1-200000000000011-1-111000000
χ3222222-2-2222-22-2-2-1222-1-1-12-22-111-1-1-111-1-1-2-20000-2-2-2-2221111-211211-1-12000000000000-1-111-1-1000000
χ332-22-22002-2-2000022-2-22-2-2200200-22-20000002-22i−2i002i−2i002i2i−2i−2i0000000000000002-22i−2i00000000000000
χ342-22-22002-2-2000022-2-22-2-2200200-22-20000002-2−2i2i00−2i2i00−2i−2i2i2i0000000000000002-2−2i2i00000000000000
χ352-22-22002-2-2000022-2-22-2-2200200-22-2000000-222i−2i00−2i2i00−2i−2i2i2i000000000000000-222i−2i00000000000000
χ362-22-22002-2-2000022-2-22-2-2200200-22-2000000-22−2i2i002i−2i002i2i−2i−2i000000000000000-22−2i2i00000000000000
χ372-2-2222i−2i-2-22002i−2i22-22-2-22-2002002-2-22i−2i002i−2i00002i−2i002-2000000002i−2i000000000000000002i−2i2-2000000
χ382-2-2222i−2i-2-22002i−2i22-22-2-22-2002002-2-22i−2i002i−2i0000−2i2i00-22000000002i−2i00000000000000000−2i2i-22000000
χ392-2-2222i−2i-2-22002i−2i-12-2211-1-200-1−i3i3-111−ii3−32i−2i00002i−2i002-2−i3i3−i3i30−i3i30−ii3−300000000000003−3−ii-11000000
χ402-2-2222i−2i-2-22002i−2i-12-2211-1-200-1−i3i3-111−ii3−32i−2i0000−2i2i00-22i3−i3i3−i30−i3i30−ii3−30000000000000−33i−i1-1000000
χ412-2-2222i−2i-2-22002i−2i-12-2211-1-200-1i3−i3-111−ii−332i−2i00002i−2i002-2i3−i3i3−i30i3−i30−ii−330000000000000−33−ii-11000000
χ422-2-2222i−2i-2-22002i−2i-12-2211-1-200-1i3−i3-111−ii−332i−2i0000−2i2i00-22−i3i3−i3i30i3−i30−ii−3300000000000003−3i−i1-1000000
χ432-2-222−2i2i-2-2200−2i2i22-22-2-22-2002002-2-2−2i2i00−2i2i00002i−2i00-2200000000−2i2i000000000000000002i−2i-22000000
χ442-2-222−2i2i-2-2200−2i2i22-22-2-22-2002002-2-2−2i2i00−2i2i0000−2i2i002-200000000−2i2i00000000000000000−2i2i2-2000000
χ452-2-222−2i2i-2-2200−2i2i-12-2211-1-200-1−i3i3-111i−i−33−2i2i00002i−2i00-22i3−i3i3−i30−i3i30i−i−3300000000000003−3−ii1-1000000
χ462-2-222−2i2i-2-2200−2i2i-12-2211-1-200-1−i3i3-111i−i−33−2i2i0000−2i2i002-2−i3i3−i3i30−i3i30i−i−330000000000000−33i−i-11000000
χ472-2-222−2i2i-2-2200−2i2i-12-2211-1-200-1i3−i3-111i−i3−3−2i2i00002i−2i00-22−i3i3−i3i30i3−i30i−i3−30000000000000−33−ii1-1000000
χ482-2-222−2i2i-2-2200−2i2i-12-2211-1-200-1i3−i3-111i−i3−3−2i2i0000−2i2i002-2i3−i3i3−i30i3−i30i−i3−300000000000003−3i−i-11000000
χ4944444444444444-2-2-2-2-2-2-2-2441-2-2111-2-2-2-2-2-200000000000000-211-211110000000000000000000000000
χ504444444444-4-444-2-2-2-2-2-2-2-2-4-4122111-2-222-2-2000000000000002-1-1211-1-10000000000000000000000000
χ5144444-4-44444-4-4-4-2-2-2-2-2-2-2-24-41-2-211122222200000000000000-2112-1-1-1-10000000000000000000000000
χ5244444-4-4444-44-4-4-2-2-2-2-2-2-2-2-4412211122-2-222000000000000002-1-1-2-1-1110000000000000000000000000
χ5344-4-4400-44-40000444-4-44-4-400400-4-4400000000000000000000000000000000000000000000000000000
χ5444-4-4400-44-400004-2-22-44-4200-20022-20000000000000000000000000000000000000000000000023−230000
χ5544-4-4400-44-400004-2-22-44-4200-20022-200000000000000000000000000000000000000000000000−23230000
χ5644-4-4400-44-40000-244-42-22-400-20022-2000000000000000023−23−2323000000000000000000000000000000000
χ5744-4-4400-44-40000-244-42-22-400-20022-20000000000000000−232323−23000000000000000000000000000000000
χ584-44-44004-4-400004-2224-4-4-200-2002-220000004-4000000000000000000000000000-220000000000000000
χ594-44-44004-4-400004-2224-4-4-200-2002-22000000-440000000000000000000000000002-20000000000000000
χ604-44-44004-4-40000-24-4-4-222400-2002-220000000000004i−4i00−2i−2i2i2i000000000000000000000000000000000
χ614-44-44004-4-40000-24-4-4-222400-2002-22000000000000−4i4i002i2i−2i−2i000000000000000000000000000000000
χ624-4-4444i−4i-4-44004i−4i4-22-2-4-44200-200-2224i−4i00−2i2i000000000000000000−2i2i000000000000000000000000000
χ634-4-4444i−4i-4-44004i−4i-2-22-222-22001−2i32i31-1-1−2i2i23−23−2i2i000000000000000i3−i30i−i−330000000000000000000000000
χ644-4-4444i−4i-4-44004i−4i-2-22-222-220012i3−2i31-1-1−2i2i−2323−2i2i000000000000000−i3i30i−i3−30000000000000000000000000
χ654-4-444−4i4i-4-4400−4i4i4-22-2-4-44200-200-222−4i4i002i−2i0000000000000000002i−2i000000000000000000000000000
χ664-4-444−4i4i-4-4400−4i4i-2-22-222-22001−2i32i31-1-12i−2i−23232i−2i000000000000000i3−i30−ii3−30000000000000000000000000
χ674-4-444−4i4i-4-4400−4i4i-2-22-222-220012i3−2i31-1-12i−2i23−232i−2i000000000000000−i3i30−ii−330000000000000000000000000
χ686666-366-3-3-366-3-300000000-3-30000000000000022000000000000000000000202200-1-1-1-100000000-1-100
χ696666-366-3-3-366-3-300000000-3-300000000000000-2-2000000000000000000000-20-2-2001111000000001100
χ706666-366-3-3-3-6-6-3-300000000330000000000000022000000000000000000000-202-200-1-1-1-1000000001100
χ716666-366-3-3-3-6-6-3-3000000003300000000000000-2-200000000000000000000020-2200111100000000-1-100
χ726666-3-6-6-3-3-36-63300000000-330000000000000022000000000000000000000-20-2200-1-111000000001-100
χ736666-3-6-6-3-3-36-63300000000-3300000000000000-2-2000000000000000000000202-20011-1-100000000-1100
χ746666-3-6-6-3-3-3-6633000000003-3000000000000002200000000000000000000020-2-200-1-11100000000-1100
χ756666-3-6-6-3-3-3-6633000000003-300000000000000-2-2000000000000000000000-20220011-1-1000000001-100
χ7688-8-8800-88-80000-4-4-444-44400200-2-2200000000000000000000000000000000000000000000000000000
χ778-88-88008-8-80000-4-444-444-400200-22-200000000000000000000000000000000000000000000000000000
χ781212-12-12-6006-660000000000000000000000000000000000000000000000000000000000023−23000000000000
χ791212-12-12-6006-6600000000000000000000000000000000000000000000000000000000000−2323000000000000
χ8012-1212-12-600-66600000000000000000000000000004i−4i000000000000000000000000000−2i2i00000000000000
χ8112-1212-12-600-6660000000000000000000000000000−4i4i0000000000000000000000000002i−2i00000000000000
χ8212-12-1212-612i−12i66-600−6i6i000000000000000000000000000000000000000000000000000000000000000000000
χ8312-12-1212-6−12i12i66-6006i−6i000000000000000000000000000000000000000000000000000000000000000000000

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