Finite Group Databasebeta

← Group #13180538

Character table — Group #13180538

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112223344444688888899121212121212121216161818181818181824242424242424242424272736363636363636363648484848545454545472727272
order122364433666433666622224412121212662444466666612121212121244224461212121266121244444661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-11-11111111-1-1-1-1111-11-11-1111-1111-11-11-1-1-1-11-11-11-1-1-1-11-11-1
χ3111111111111111111111-11-111111111-1-1-1-111-11-11-1111-1111-11-111-1-1-1-1-11-111-1-1-1-1-11-11
χ4111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-111-1-111-1-1-1-111111-1-1-1-111111-1-1-1-1
χ511111-1-111111-1111111111111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1
χ611111-1-111111-1111111111-11-1-1-1-1-1111-1-1-1-1111-11-11-1-1-11-1-1-1-11-111-1-1-1-11-11-1-11111-11-11
χ711111-1-111111-111111111-11-11-1-1-1-1111-1-1-1-111-11-11-11-1-1-11-1-11-11-11-1-1-1-1-11-11-111111-11-1
χ811111-1-111111-111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-11111
χ911-1111111-111-111-1-1111111-1-11111-1-1-111-1-1111111-1-1-1-1-1-111-1-111-111-1-111-1-1-111-1-1-1-111
χ1011-1111111-111-111-1-111111-1-111111-1-1-1-1-111111-11-1-11-1-1-1111-111-1-1-1-1111-1-11-1-1-111-111-1
χ1111-1111111-111-111-1-11111-111-11111-1-1-1-1-11111-11-111-1-1-11-1111-1-11-1-1-111-111-1-1-1-1111-1-11
χ1211-1111111-111-111-1-11111-1-1111111-1-1-111-1-111-1-1-1-111-1-1111111-1-1-111-1-1-1-111-111-1-111-1-1
χ1311-111-1-111-111111-1-1111111-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-111-1-1-111-1-111-1-11-1-11111-1-1
χ1411-111-1-111-111111-1-111111-1-11-1-1-1-1-1-1-1-1-111111-11-1-1111-11-1-11-1-11-1-1-1111-1-11111-1-11-1-11
χ1511-111-1-111-111111-1-11111-111-1-1-1-1-1-1-1-1-1-11111-11-111-1111-1-1-1-111-1-1-1-111-111-1111-1-1-111-1
χ1611-111-1-111-111111-1-11111-1-111-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-111-111-1-1-1-1111-1-111-1-111
χ172222222222222222222-2-20000222222-20000-2-20000002200-2-20000-200000000-200000000
χ1822222-2-222222-2222222-2-20000-2-2-2-222-20000-2-2000000-2-200220000-200000000200000000
χ19222-1-10022-1220-1-122-1-12222220000-1-122222-1-1-1-122-1-10022000000-1-1-1-1-1-1-1-1-1000000000
χ20222-1-10022-1220-1-122-1-1222-22-20000-1-12-2-2-2-2-1-1-112-2-11002-2000000-11111-11-11000000000
χ21222-1-10022-1220-1-122-1-122-22-220000-1-12-2-2-2-2-1-11-1-221-100-22000000-111111-11-1000000000
χ22222-1-10022-1220-1-122-1-122-2-2-2-20000-1-122222-1-111-2-21100-2-2000000-1-1-1-1-11111000000000
χ2322-2222222-222-222-2-222-2-200002222-2-220000-2-2000000-2-200-2-20000200000000200000000
χ2422-222-2-222-222222-2-222-2-20000-2-2-2-2-2-220000-2-20000002200220000200000000-200000000
χ2522-2-1-100221220-1-1-2-2-1-12222-2-2000011-222-2-2-1-1-1-1221100-2-20000001-1-111-1-111000000000
χ2622-2-1-100221220-1-1-2-2-1-1222-2-22000011-2-2-222-1-1-112-21-100-22000000111-1-1-111-1000000000
χ2722-2-1-100221220-1-1-2-2-1-122-222-2000011-2-2-222-1-11-1-22-11002-2000000111-1-11-1-11000000000
χ2822-2-1-100221220-1-1-2-2-1-122-2-222000011-222-2-2-1-111-2-2-1-100220000001-1-11111-1-1000000000
χ292-202-22i−2i220-2-202200-2-22-200002i2i−2i−2i0002-200-2200000000002i−2i000002-200000002i−2i000000
χ302-202-22i−2i220-2-202200-2-22-200002i2i−2i−2i000-2200-2200000000002i−2i00000-220000000−2i2i000000
χ312-202-22i−2i220-2-202200-2-2-2200002i2i−2i−2i000002i−2i2-20000000000−2i2i00000002i−2i00000002-20000
χ322-202-22i−2i220-2-202200-2-2-2200002i2i−2i−2i00000−2i2i2-20000000000−2i2i0000000−2i2i0000000-220000
χ332-202-2−2i2i220-2-202200-2-22-20000−2i−2i2i2i0002-200-220000000000−2i2i000002-20000000−2i2i000000
χ342-202-2−2i2i220-2-202200-2-22-20000−2i−2i2i2i000-2200-220000000000−2i2i00000-2200000002i−2i000000
χ352-202-2−2i2i220-2-202200-2-2-220000−2i−2i2i2i000002i−2i2-200000000002i−2i00000002i−2i0000000-220000
χ362-202-2−2i2i220-2-202200-2-2-220000−2i−2i2i2i00000−2i2i2-200000000002i−2i0000000−2i2i00000002-20000
χ3744444441-241-241-21-21-20002021-21-21-20000000020-1021-20-1000202000000-10-1000000-10-1
χ3844444441-241-241-21-21-2000-20-21-21-21-200000000-2010-21-201000-20-2000000101000000101
χ394444444-214-214-21-21-21002020-21-21-21000000020-1020-21-1000202000000-10-1000000-10-10
χ404444444-214-214-21-21-2100-20-20-21-21-210000000-2010-20-211000-20-20000001010000001010
χ4144444-4-41-241-2-41-21-21-2000202-12-121-20000000020-102-120-1000-20-2000000-10-1000000101
χ4244444-4-41-241-2-41-21-21-2000-20-2-12-121-200000000-2010-2-1201000202000000101000000-10-1
χ4344444-4-4-214-21-4-21-21-210020202-12-1-21000000020-10202-1-1000-20-2000000-10-10000001010
χ4444444-4-4-214-21-4-21-21-2100-20-202-12-1-210000000-2010-202-11000202000000101000000-10-10
χ45444-2-20044-2440-2-244-2-2-4-400000000-2-2-40000220000000000000000200000000000000000
χ4644-444441-2-41-2-41-2-121-200020-21-21-2-120000000020-10-2-1201000-202000000-10100000010-1
χ4744-444441-2-41-2-41-2-121-2000-2021-21-2-1200000000-20102-120-100020-200000010-1000000-101
χ4844-44444-21-4-21-4-212-1-210020-20-21-212-1000000020-10-202-11000-202000000-10100000010-10
χ4944-44444-21-4-21-4-212-1-2100-2020-21-212-10000000-2010202-1-100020-200000010-1000000-1010
χ5044-444-4-41-2-41-241-2-121-200020-2-12-12-120000000020-10-21-20100020-2000000-101000000-101
χ5144-444-4-41-2-41-241-2-121-2000-202-12-12-1200000000-201021-20-1000-20200000010-100000010-1
χ5244-444-4-4-21-4-214-212-1-210020-202-12-12-1000000020-10-20-21100020-2000000-101000000-1010
χ5344-444-4-4-21-4-214-212-1-2100-20202-12-12-10000000-201020-21-1000-20200000010-100000010-10
χ5444-4-2-200442440-2-2-4-4-2-2-4-4000000002240000220000000000000000-200000000000000000
χ554-40-2200440-4-40-2-200224-4000000000004-4002-200000000000000000-22000000000000000
χ564-40-2200440-4-40-2-200224-400000000000-44002-2000000000000000002-2000000000000000
χ574-40-2200440-4-40-2-20022-4400000000000004i−4i-220000000000000000000−2i2i0000000000000
χ584-40-2200440-4-40-2-20022-440000000000000−4i4i-2200000000000000000002i−2i0000000000000
χ59888-4-4002-4-42-40-122-4-120004040000-1200000000-20-20-2000-2000000000000101000000000
χ60888-4-4002-4-42-40-122-4-12000-40-40000-1200000000202020002000000000000-10-1000000000
χ61888-4-400-42-4-4202-1-422-100404000002-10000000-20-20-2000-20000000000001010000000000
χ62888-4-400-42-4-4202-1-422-100-40-4000002-10000000202020002000000000000-10-10000000000
χ6388-8-4-4002-442-40-12-24-1200040-400001-200000000-20-202000200000000000010-1000000000
χ6488-8-4-4002-442-40-12-24-12000-40400001-2000000002020-2000-2000000000000-101000000000
χ6588-8-4-400-424-4202-14-22-10040-400000-210000000-20-202000200000000000010-10000000000
χ6688-8-4-400-424-4202-14-22-100-40400000-2100000002020-2000-2000000000000-1010000000000
χ678-808-88i−8i2-40-2402-400-240000002i−4i−2i4i0000000000000000000000000000000000000000000
χ688-808-88i−8i-4204-20-42004-2000000−4i2i4i−2i0000000000000000000000000000000000000000000
χ698-808-8−8i8i2-40-2402-400-24000000−2i4i2i−4i0000000000000000000000000000000000000000000
χ708-808-8−8i8i-4204-20-42004-20000004i−2i−4i2i0000000000000000000000000000000000000000000
χ7116-160-88004-80-480-24002-400000000000000000000000000000000000000000000000000000
χ7216-160-8800-8408-404-200-4200000000000000000000000000000000000000000000000000000

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