Finite Group Databasebeta

← Group #13180536

Character table — Group #13180536

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1122233444444466666888888899121212121212121212121212121212121618181818181818242424242424242424272736363636363636363648485472727272108108
order12236443366666222243366666222466666666121212121212624444666666661212124424446121212126124612121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111111111111111111111-1-11111-11-111-1-1-1-111111-1-11-1-1-1-1-1-1
χ311111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111111-1-11-1-1-1-111111-1-1-1-1
χ411111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-11-111-1-1111-1-1-1-1-1-11-1-11111
χ511111-1-111111111111-11111111111111111111-1-1-1-1-1-111-1-1-1-1111111111-11-1-1-1-1111-1-1-1-111-1-1-111-1-1
χ611111-1-111111111111-1111111111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-111-1-11-1-1-1-1-1-1-111-1-111
χ711111-1-11111111-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11-11-1-1-1-1-1-11111111-1-1-1-1-111
χ811111-1-11111111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1
χ911-1111111-1-1-11111-1-1-111-11-1-11111-111-1-111-1-11111-1-1-1-111-1-1111111-1-1-1-1-111-111-1-111-1-11-1-1-111-11-1
χ1011-1111111-1-1-11111-1-1-111-11-1-1111-1111-1-111-1-11111-1-1-1-111-1-111-1-111-1-11-11111-1-11-111-1-1-11-11-1-11-11
χ1111-1111111-1-1-111-1-111-111-11-1-11111-1-1-111-1-1111111-1-1-1-1-1-1111111-1-111-1-1-111-11-11-1-1-1111-1-1-11-11-11
χ1211-1111111-1-1-111-1-111-111-11-1-1111-11-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-1111-11111-11-1-1-1-111-11-11-11-11-1
χ1311-111-1-111-1-1-11111-1-1111-11-1-11111-111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-11-1-1-11-11-1-1-1-1111-111-11-1-11
χ1411-111-1-111-1-1-11111-1-1111-11-1-1111-1111-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1111-1-1-11-11-1-1-111-111-11-111-1
χ1511-111-1-111-1-1-111-1-111111-11-1-11111-1-1-111-1-111-1-1-1-111-1-111-1-11111-1-111-11-1-1-11-1-11-111-1-11-111-1-111-1
χ1611-111-1-111-1-1-111-1-111111-11-1-1111-11-1-111-1-111-1-1-1-111-1-111-1-111-1-1-1-111111-1-1-111-1-111-1-1-111-111-1-11
χ1722222222222222000022222222-2-200000000002222222-20000-2-2000000020-2-20000-2000000-2000000
χ1822222-2-222222220000-22222222-2-20000000000-2-2-2-2-2-22-20000-2-20000000-20220000-20000002000000
χ19222-1-10022-1222222220-1-12-1-1-1-12222-1-1-1-12222000000-120000-1-1-12-1-1-1-1-102000022-10000-1-1000-1-100
χ20222-1-10022-1222222220-1-12-1-1-1-122-2-2-1-1-1-12222000000-120000-1-11-2-1-1-1-110-20000-2-2-10000110001100
χ21222-1-10022-12222-2-2-2-20-1-12-1-1-1-122221111-2-2-2-2000000-120000-1-1-121111-1020000-2-2-10000-1-10001100
χ22222-1-10022-12222-2-2-2-20-1-12-1-1-1-122-2-21111-2-2-2-2000000-120000-1-11-2111110-2000022-1000011000-1-100
χ2322-2222222-2-2-2220000-222-22-2-22-2-200000000002222-2-2-220000-2-20000000-20-2-2000020000002000000
χ2422-222-2-222-2-2-2220000222-22-2-22-2-20000000000-2-2-2-222-220000-2-20000000202200002000000-2000000
χ2522-2-1-100221-2-22222-2-20-1-1-2-111-1222-2-1-11122-2-20000001-20000-1-1-12-1-11110-200002-210000-11000-1100
χ2622-2-1-100221-2-22222-2-20-1-1-2-111-122-22-1-11122-2-20000001-20000-1-11-2-1-111-1020000-22100001-10001-100
χ2722-2-1-100221-2-222-2-2220-1-1-2-111-1222-211-1-1-2-2220000001-20000-1-1-1211-1-110-20000-2210000-110001-100
χ2822-2-1-100221-2-222-2-2220-1-1-2-111-122-2211-1-1-2-2220000001-20000-1-11-211-1-1-10200002-2100001-1000-1100
χ292-202-22i−2i22000-2-2002-20220-200-22-200002-2002-22i−2i2i−2i0000002i−2i2-200002-20002i−2i00000002i−2i000000000
χ302-202-22i−2i22000-2-200-220220-200-22-20000-2200-222i−2i2i−2i000000−2i2i2-20000-220002i−2i0000000−2i2i000000000
χ312-202-22i−2i22000-2-22-2000220-200-2-22002-2002-2002i−2i2i−2i00002i−2i00-22002-200000−2i2i000002i−2i00000000000
χ322-202-22i−2i22000-2-2-22000220-200-2-2200-2200-22002i−2i2i−2i0000−2i2i00-2200-2200000−2i2i00000−2i2i00000000000
χ332-202-2−2i2i22000-2-2002-20220-200-22-200002-2002-2−2i2i−2i2i000000−2i2i2-200002-2000−2i2i0000000−2i2i000000000
χ342-202-2−2i2i22000-2-200-220220-200-22-20000-2200-22−2i2i−2i2i0000002i−2i2-20000-22000−2i2i00000002i−2i000000000
χ352-202-2−2i2i22000-2-22-2000220-200-2-22002-2002-200−2i2i−2i2i0000−2i2i00-22002-2000002i−2i00000−2i2i00000000000
χ362-202-2−2i2i22000-2-2-22000220-200-2-2200-2200-2200−2i2i−2i2i00002i−2i00-2200-22000002i−2i000002i−2i00000000000
χ3744444441-2411-2122224-21-2111-200002222-1-1-1-1-2-21111-2022220000-1-1-1-10-200000000-1-1-1-1000000000
χ3844444441-2411-21-2-2-2-24-21-2111-20000-2-2-2-21111-2-21111-20-2-2-2-2000011110-2000000001111000000000
χ394444444-214-2-21-2000041-21-2-2-2100220000000011-2-2-2-2100000002-1000021-100220000000-1-10-1-10000
χ404444444-214-2-21-2000041-21-2-2-2100-2-20000000011-2-2-2-210000000-210000-21100-2-20000000110110000
χ4144444-4-41-2411-212222-4-21-2111-200002222-1-1-1-122-1-1-1-1-20-2-2-2-20000-1-1-1-102000000001111000000000
χ4244444-4-41-2411-21-2-2-2-2-4-21-2111-20000-2-2-2-2111122-1-1-1-1-202222000011110200000000-1-1-1-1000000000
χ4344444-4-4-214-2-21-20000-41-21-2-2-21002200000000-1-12222100000002-100002-1-100-2-20000000-1-10110000
χ4444444-4-4-214-2-21-20000-41-21-2-2-2100-2-200000000-1-1222210000000-210000-2-1100220000000110-1-10000
χ45444-2-20044-2444400000-2-24-2-2-2-2-4-40000000000000000-2-400002200000000000000020000000000000
χ4644-444441-2-4-1-1-2122-2-2-4-2121-1-1-2000022-2-2-1-111-2-211-1-12022-2-20000-1-1110200000000-1-111000000000
χ4744-444441-2-4-1-1-21-2-222-4-2121-1-1-20000-2-22211-1-1-2-211-1-120-2-222000011-1-1020000000011-1-1000000000
χ4844-44444-21-4221-20000-41-2-1-2221002-20000000011-2-222-100000002-10000-2-1100-220000000-1101-10000
χ4944-44444-21-4221-20000-41-2-1-222100-220000000011-2-222-10000000-2100002-1-1002-200000001-10-110000
χ5044-444-4-41-2-4-1-1-2122-2-24-2121-1-1-2000022-2-2-1-11122-1-11120-2-2220000-1-1110-20000000011-1-1000000000
χ5144-444-4-41-2-4-1-1-21-2-2224-2121-1-1-20000-2-22211-1-122-1-1112022-2-2000011-1-10-200000000-1-111000000000
χ5244-444-4-4-21-4221-2000041-2-1-2221002-200000000-1-122-2-2-100000002-10000-211002-20000000-110-110000
χ5344-444-4-4-21-4221-2000041-2-1-222100-2200000000-1-122-2-2-10000000-21000021-100-2200000001-101-10000
χ5444-4-2-200442-4-44400000-2-2-4-222-2-4-4000000000000000024000022000000000000000-20000000000000
χ554-404-44i−4i1-203-32-12-22-20-210-13-3200002-22-2-11-11−2i2ii−i3i−3i002i−2i2i−2i0000-11-110000000000−ii−ii000000000
χ564-404-44i−4i1-203-32-1-22-220-210-13-320000-22-221-11-1−2i2ii−i3i−3i00−2i2i−2i2i00001-11-10000000000i−ii−i000000000
χ574-404-44i−4i1-20-332-12-2-220-210-1-33200002-2-22-111-1−2i2ii−i−3i3i002i−2i−2i2i0000-111-10000000000−iii−i000000000
χ584-404-44i−4i1-20-332-1-222-20-210-1-3320000-222-21-1-11−2i2ii−i−3i3i00−2i2i2i−2i00001-1-110000000000i−i−ii000000000
χ594-404-4−4i4i1-203-32-12-22-20-210-13-3200002-22-2-11-112i−2i−ii−3i3i00−2i2i−2i2i0000-11-110000000000i−ii−i000000000
χ604-404-4−4i4i1-203-32-1-22-220-210-13-320000-22-221-11-12i−2i−ii−3i3i002i−2i2i−2i00001-11-10000000000−ii−ii000000000
χ614-404-4−4i4i1-20-332-12-2-220-210-1-33200002-2-22-111-12i−2i−ii3i−3i00−2i2i2i−2i0000-111-10000000000i−i−ii000000000
χ624-404-4−4i4i1-20-332-1-222-20-210-1-3320000-222-21-1-112i−2i−ii3i−3i002i−2i−2i2i00001-1-110000000000−iii−i000000000
χ634-40-220044000-4-4004-40-2-2020024-40000-22004-4000000000000-220000-2200000000000000000000000
χ644-40-220044000-4-400-440-2-2020024-400002-200-44000000000000-2200002-200000000000000000000000
χ654-40-220044000-4-44-4000-2-202002-4400-22004-4000000000000002-200-220000000000000000000000000
χ664-40-220044000-4-4-44000-2-202002-44002-200-44000000000000002-2002-20000000000000000000000000
χ67888-4-4002-4-422-42444402-1-4-1-1-120000-2-2-2-2-2-2-2-20000002000000000111100000000000000000000000
χ68888-4-4002-4-422-42-4-4-4-402-1-4-1-1-120000222222220000002000000000-1-1-1-100000000000000000000000
χ69888-4-400-42-4-4-42-400000-122222-1004400000000000000-10000000-2-20000-20-200000000000110000000
χ70888-4-400-42-4-4-42-400000-122222-100-4-400000000000000-1000000022000020200000000000-1-10000000
χ7188-8-4-4002-44-2-2-4244-4-402-14-11120000-2-222-2-222000000-200000000011-1-100000000000000000000000
χ7288-8-4-4002-44-2-2-42-4-44402-14-1112000022-2-222-2-2000000-2000000000-1-11100000000000000000000000
χ7388-8-4-400-424442-400000-12-22-2-2-1004-40000000000000010000000-2-20000202000000000001-10000000
χ7488-8-4-400-424442-400000-12-22-2-2-100-440000000000000010000000220000-20-200000000000-110000000
χ758-808-88i−8i-42000-24000002-40400-20000000000002i−2i−4i4i000000000000000000000000000000000000000
χ768-808-8−8i8i-42000-24000002-40400-2000000000000−2i2i4i−4i000000000000000000000000000000000000000
χ778-80-44002-406-64-24-44-402-101-33-20000-22-22-22-2200000000000000001-11-100000000000000000000000
χ788-80-44002-406-64-2-44-4402-101-33-200002-22-22-22-20000000000000000-11-1100000000000000000000000
χ798-80-44002-40-664-24-4-4402-1013-3-20000-222-2-222-200000000000000001-1-1100000000000000000000000
χ808-80-44002-40-664-2-444-402-1013-3-200002-2-222-2-220000000000000000-111-100000000000000000000000
χ8116-160-8800-84000-4800000-240-40020000000000000000000000000000000000000000000000000000000

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