Finite Group Databasebeta

← Group #13149491

Character table — Group #13149491

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order1222344666441212336666661212366612121212121212124444121212121212121212121212244444444412121212121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11-1-1-1-11-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-111-1-11-1-1-1-1-1-111-1-111-1-1-1-11-1-11
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1
χ51111111111-1-11111111111-1-111111111-1-1-1-111111111-1-1-1-111-1-11-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ61111111111-1-11111111111-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-11-11111111-1-11111-1-1-1-1-1-1
χ71111111111-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-111-1-111111-1-111-1-1-1-1111-1-11
χ81111111111-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11-1111-1-1-1-1-1111111-1-111-111-1
χ911111-1-11111-1-1-1111111111-11111-1-1-1-111-1-111-1-111111-1-1-1-1-1111-11-1-1111-1-111-1-111-1-1-1-1-1-11111-1-1
χ1011111-1-11111-1-1-1111111111-11111-1-1-1-111-1-111-1-111111-1-1-1-1-111-1-1-111-11-111-1-111-1-1-1-111-1-111-1-111
χ1111111-1-11111-1-1-1111111111-11111-1-1-1-111-1-1-1-111-1-1-1-11-1-1-1-1-11111-1-1-1-1-1111-1-1111111-1-111-1-11-11-1
χ1211111-1-11111-1-1-1111111111-11111-1-1-1-111-1-1-1-111-1-1-1-11-1-1-1-1-111-111111-1-1-1-111-1-1-1-1111111-1-1-11-11
χ1311111-1-1111-11-1-111111111-111111-1-1-1-1-1-11111-1-11111-1111-1-1-1-1111-11-1-1-1-11-1-111-1-11111-1-1-1-111-1-1
χ1411111-1-1111-11-1-111111111-111111-1-1-1-1-1-11111-1-11111-1111-1-1-1-1-11-11-11-111-111-1-11111-1-1-1-1-1-1-1-111
χ1511111-1-1111-11-1-111111111-111111-1-1-1-1-1-111-1-111-1-1-1-1-1111-1-1-1-11-1-1-1111-11-111-1-1-1-1-1-11111111-11-1
χ1611111-1-1111-11-1-111111111-111111-1-1-1-1-1-111-1-111-1-1-1-1-1111-1-1-1-1-1-111-1-111-11-1-11111-1-1-1-11111-11-11
χ17222222222222222-1-12-12-1222-1-1-1-1-1-122222200000000-1-1-1-1-1-1-1-120022002000000-1-100-1-10000-100-1
χ18222222222222222-1-12-12-1222-1-1-1-1-1-122222200000000-1-1-1-1-1-1-1-1-200-2-200-200000011001100001001
χ1922222222222222-122-12-12-122-1-1-1-122-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-10200002000000000-1-100-1-1-1-10000
χ2022222222222222-122-12-12-122-1-1-1-122-1-1-1-1-1-1-2-2-2-2111122-1-1-1-1-1-10-20000-2000000000110011110000
χ212222222222-2-2222-1-12-12-12-2-2-1-1-1-1-1-122-2-2-2-2000000001111-1-1112002-200-20000001100110000-100-1
χ222222222222-2-2222-1-12-12-12-2-2-1-1-1-1-1-122-2-2-2-2000000001111-1-111-200-22002000000-1-100-1-100001001
χ232222222222-2-222-122-12-12-1-2-2-1-1-1-122-1-111112222-1-1-1-1-2-211-1-1110-20000-20000000001100-1-1110000
χ242222222222-2-222-122-12-12-1-2-2-1-1-1-122-1-11111-2-2-2-21111-2-211-1-1110200002000000000-1-10011-1-10000
χ2522222-2-22222-2-2-22-1-12-12-122-2-1-1-1-111-2-222-2-200000000-111111-1-1200-2-2002000000-1-100110000-1001
χ2622222-2-22222-2-2-22-1-12-12-122-2-1-1-1-111-2-222-2-200000000-111111-1-1-2002200-20000001100-1-10000100-1
χ2722222-2-22222-2-2-2-122-12-12-12-2-1-1-1-1-2-211-1-11122-2-2-1-1-1-12-21111-1-10-200002000000000110011-1-10000
χ2822222-2-22222-2-2-2-122-12-12-12-2-1-1-1-1-2-211-1-111-2-22211112-21111-1-1020000-2000000000-1-100-1-1110000
χ2922222-2-2222-22-2-22-1-12-12-12-22-1-1-1-111-2-2-2-222000000001-1-1-11111200-2200-20000001100-1-10000-1001
χ3022222-2-2222-22-2-22-1-12-12-12-22-1-1-1-111-2-2-2-222000000001-1-1-11111-2002-2002000000-1-100110000100-1
χ3122222-2-2222-22-2-2-122-12-12-1-22-1-1-1-1-2-21111-1-122-2-2-1-1-1-1-22-1-11111020000-2000000000-1-10011110000
χ3222222-2-2222-22-2-2-122-12-12-1-22-1-1-1-1-2-21111-1-1-2-2221111-22-1-111110-2000020000000001100-1-1-1-10000
χ332-2-2222i−2i-2-22002i−2i22-2-22-2-22002-22-22i−2i2i−2i00002i−2i2-22i2i−2i−2i00002i−2i00000000000000000000002-2000000
χ342-2-2222i−2i-2-22002i−2i22-2-22-2-22002-22-22i−2i2i−2i0000−2i2i-22−2i−2i2i2i00002i−2i0000000000000000000000-22000000
χ352-2-2222i−2i-2-22002i−2i-12-2121-2-100-11-112i−2i−ii3−3−i3i32i−2i2-2−i−iii00−i3i3−ii3−300000000000000003−300-11−i3i30000
χ362-2-2222i−2i-2-22002i−2i-12-2121-2-100-11-112i−2i−ii3−3−i3i3−2i2i-22ii−i−i00−i3i3−ii3−30000000000000000−33001-1i3−i30000
χ372-2-2222i−2i-2-22002i−2i-12-2121-2-100-11-112i−2i−ii−33i3−i32i−2i2-2−i−iii00i3−i3−ii−330000000000000000−3300-11i3−i30000
χ382-2-2222i−2i-2-22002i−2i-12-2121-2-100-11-112i−2i−ii−33i3−i3−2i2i-22ii−i−i00i3−i3−ii−3300000000000000003−3001-1−i3i30000
χ392-2-222−2i2i-2-2200−2i2i22-2-22-2-22002-22-2−2i2i−2i2i00002i−2i-222i2i−2i−2i0000−2i2i0000000000000000000000-22000000
χ402-2-222−2i2i-2-2200−2i2i22-2-22-2-22002-22-2−2i2i−2i2i0000−2i2i2-2−2i−2i2i2i0000−2i2i00000000000000000000002-2000000
χ412-2-222−2i2i-2-2200−2i2i-12-2121-2-100-11-11−2i2ii−i3−3i3−i32i−2i-22−i−iii00i3−i3i−i3−30000000000000000−33001-1−i3i30000
χ422-2-222−2i2i-2-2200−2i2i-12-2121-2-100-11-11−2i2ii−i3−3i3−i3−2i2i2-2ii−i−i00i3−i3i−i3−300000000000000003−300-11i3−i30000
χ432-2-222−2i2i-2-2200−2i2i-12-2121-2-100-11-11−2i2ii−i−33−i3i32i−2i-22−i−iii00−i3i3i−i−3300000000000000003−3001-1i3−i30000
χ442-2-222−2i2i-2-2200−2i2i-12-2121-2-100-11-11−2i2ii−i−33−i3i3−2i2i2-2ii−i−i00−i3i3i−i−330000000000000000−3300-11−i3i30000
χ4544444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-200000000-2-21111110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-41111-2-2-2-222220000000022-1-111-1-10000000000000000000000000000
χ4744444-4-44444-4-4-4-2-2-2-2-2-2-2-24-411112222-2-22200000000-22-1-1-1-1110000000000000000000000000000
χ4844444-4-4444-44-4-4-2-2-2-2-2-2-2-2-441111222222-2-2000000002-211-1-1-1-10000000000000000000000000000
χ4944-4-4400-44-40000444-4-44-4-4004-4-440000000000000000000000000000000000000000000000000000
χ5044-4-4400-44-400004-2-2-4242-400-222-200000000000000000000000000000000000000000023−2300000000
χ5144-4-4400-44-400004-2-2-4242-400-222-2000000000000000000000000000000000000000000−232300000000
χ5244-4-4400-44-40000-2442-4-2-4200-222-200000000000023−2323−23000000000000000000000000000000000000
χ5344-4-4400-44-40000-2442-4-2-4200-222-2000000000000−2323−2323000000000000000000000000000000000000
χ544-44-44004-4-4000044-44-4-44-40044-4-40000000000000000000000000000000000000000000000000000
χ554-44-44004-4-400004-2242-4-2-400-2-2220000000000000000000000000000000000000023−23000000000000
χ564-44-44004-4-400004-2242-4-2-400-2-22200000000000000000000000000000000000000−2323000000000000
χ574-44-44004-4-40000-24-4-2-424200-2-222000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ584-44-44004-4-40000-24-4-2-424200-2-2220000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ594-4-4444i−4i-4-44004i−4i4-22-4-2-42400-22-22−2i2i4i−4i0000000000000000−2i2i000000000000000000000000000000
χ604-4-4444i−4i-4-44004i−4i-2-222-222-2001-11-1−2i2i−2i2i23−23−2i32i30000000000i3−i3i−i−330000000000000000000000000000
χ614-4-4444i−4i-4-44004i−4i-2-222-222-2001-11-1−2i2i−2i2i−23232i3−2i30000000000−i3i3i−i3−30000000000000000000000000000
χ624-4-444−4i4i-4-4400−4i4i4-22-4-2-42400-22-222i−2i−4i4i00000000000000002i−2i000000000000000000000000000000
χ634-4-444−4i4i-4-4400−4i4i-2-222-222-2001-11-12i−2i2i−2i23−232i3−2i30000000000−i3i3−ii−330000000000000000000000000000
χ644-4-444−4i4i-4-4400−4i4i-2-222-222-2001-11-12i−2i2i−2i−2323−2i32i30000000000i3−i3−ii3−30000000000000000000000000000
χ656666-366-3-3-366-3-300000000-3-300000000000000000000000000000020020022-1-1-1-100000000000-1-10
χ666666-366-3-3-366-3-300000000-3-3000000000000000000000000000000-200-200-2-2111100000000000110
χ676666-366-3-3-3-6-6-3-30000000033000000000000000000000000000000200-2002-2111100000000000-1-10
χ686666-366-3-3-3-6-6-3-30000000033000000000000000000000000000000-200200-22-1-1-1-100000000000110
χ696666-3-6-6-3-3-36-63300000000-33000000000000000000000000000000200200-2-2-1-11100000000000-110
χ706666-3-6-6-3-3-36-63300000000-33000000000000000000000000000000-200-2002211-1-1000000000001-10
χ716666-3-6-6-3-3-3-6633000000003-3000000000000000000000000000000200-200-2211-1-100000000000-110
χ726666-3-6-6-3-3-3-6633000000003-3000000000000000000000000000000-2002002-2-1-111000000000001-10
χ7388-8-8800-88-80000-4-4-444-444002-2-220000000000000000000000000000000000000000000000000000
χ748-88-88008-8-80000-4-44-444-440022-2-20000000000000000000000000000000000000000000000000000
χ751212-12-12-6006-6600000000000000000000000000000000000000000000000000000023−2300000000000000
χ761212-12-12-6006-66000000000000000000000000000000000000000000000000000000−232300000000000000
χ7712-1212-12-600-6660000000000000000000000000000000000000000000000000000−2i32i30000000000000000
χ7812-1212-12-600-66600000000000000000000000000000000000000000000000000002i3−2i30000000000000000
χ7912-12-1212-612i−12i66-600−6i6i000000000000000000000000000000000000000000000000000000000000000000
χ8012-12-1212-6−12i12i66-6006i−6i000000000000000000000000000000000000000000000000000000000000000000

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