Finite Group Databasebeta

← Group #13151943

Character table — Group #13151943

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order12442346121224612336612121212612366666121212121212224466121266661212121222244466688881212122424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-11-1-1111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-11-1-11-1-1-1-111-1-1-1-1-11111-1-1-1-11-11-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-11-1-1-1-1-111-1-1-1-1-1-1-11111-11-11
χ51111111111-1-11111111111-1-1111-1-111-1-111111111111-11-1-1-11-1-1-111-1111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111
χ61111111111-1-11111111111-1-1111-1-111-1-111111111111-11-1-1-11-1-1-1-1-1-1-1-11-1-111111-1-111111111-1-1-1-1
χ71111111111-1-11111111111-1-1111-1-111-1-1111-1-1-1-1-1-1-1-1-11-1-1-11-1-111-111-1-111-1-111-111-1-1-1-111111-11-1
χ81111111111-1-11111111111-1-1111-1-111-1-1111-1-1-1-1-1-1-1-1-11-1-1-11-1-11-111-11-11111-1-1-1111111-1-1-1-1-11-11
χ911-1-1-1111-1-11-1-111111-1-1-1-11-11-1-11111-1-1-1-111-11-111-1-11-111-11-1-111-1-1-11-1111-11-11-1-111-1-111-1-11-1-11
χ1011-1-1-1111-1-11-1-111111-1-1-1-11-11-1-11111-1-1-1-111-11-111-1-11-111-11-1-11-11-11-1-111-11-111-1-1-1-111-1-111-111-1
χ1111-1-1-1111-1-11-1-111111-1-1-1-11-11-1-11111-1-1-1-11-11-11-1-1111-111-11-1-1-1111-1-11-1-11-1-11-11111-1-1-1-11111-1-1
χ1211-1-1-1111-1-11-1-111111-1-1-1-11-11-1-11111-1-1-1-11-11-11-1-1111-111-11-1-1-1-1-11111-1-1-111-1-111-1-11111-1-1-1-111
χ1311-1-1-1111-1-1-11-111111-1-1-1-1-111-1-1-1-11111-1-111-11-111-1-1-1-1-1-11111-11-11-11-1-1-1-11-11111-1-111-1-1111-1-11
χ1411-1-1-1111-1-1-11-111111-1-1-1-1-111-1-1-1-11111-1-111-11-111-1-1-1-1-1-11111-1-1111-1-1-1-11-11-111111-1-111-1-1-111-1
χ1511-1-1-1111-1-1-11-111111-1-1-1-1-111-1-1-1-11111-1-11-11-11-1-111-1-1-1-11111111-1-1-1111-111-1-1-1-1-1-11111-1-111-1-1
χ1611-1-1-1111-1-1-11-111111-1-1-1-1-111-1-1-1-11111-1-11-11-11-1-111-1-1-1-111111-1-1-1111111-1-11-1-1-111-1-1-1-111-1-111
χ17222222222222222-12-122-1-122-12-1-1-1-1-1-1-1-1-122222-1-1-1-12-1-1-12-1-1-1200200-1-1-10000-1-1-1000000000000
χ18222222222222222-12-122-1-122-12-1-1-1-1-1-1-1-1-12-2-2-2-211112-1-1-12-1-1-1-200-2001110000111000000000000
χ1922222222222222-12-12-1-12222-1-1222-1222-1-1-100000000-1-1-1-1-1-1-1-100200200000220000000-1-1-1-10-10-1
χ2022222222222222-12-12-1-12222-1-1222-1222-1-1-100000000-1-1-1-1-1-1-1-100-200-200000-2-2000000011110101
χ212222222222-2-2222-12-122-1-1-2-2-12-111-1-111-1-122222-1-1-1-1-2-111-2-111-200-200-1110000-111000000000000
χ222222222222-2-2222-12-122-1-1-2-2-12-111-1-111-1-12-2-2-2-21111-2-111-2-1112002001-1-100001-1-1000000000000
χ232222222222-2-222-12-12-1-122-2-2-1-12-2-2-12-2-2-1-1-1000000001-1111-11100200200000-2-2000000011110-10-1
χ242222222222-2-222-12-12-1-122-2-2-1-12-2-2-12-2-2-1-1-1000000001-1111-11100-200-200000220000000-1-1-1-10101
χ252222-22-222200-2-222222222002-2-2002-20022-22-2-2222220-2000-200000000-2000000-200000000000000
χ262222-22-222200-2-222222222002-2-2002-20022-2-222-2-2-2-2-20-2000-2000000002000000200000000000000
χ272222-22-222200-2-22-12-122-1-100-1-21−i3i3-11−i3i3-1-1-22-2-22-1-1-1-101−i3i301−i3i30000001−i3i300001−i3i3000000000000
χ282222-22-222200-2-22-12-122-1-100-1-21−i3i3-11−i3i3-1-1-2-222-2111101−i3i301−i3i3000000-1i3−i30000-1i3−i3000000000000
χ292222-22-222200-2-22-12-122-1-100-1-21i3−i3-11i3−i3-1-1-22-2-22-1-1-1-101i3−i301i3−i30000001i3−i300001i3−i3000000000000
χ302222-22-222200-2-22-12-122-1-100-1-21i3−i3-11i3−i3-1-1-2-222-2111101i3−i301i3−i3000000-1−i3i30000-1−i3i3000000000000
χ3122-2-222-22-2-2002-22222-2-2-2-200222002-200-2-2-222-2-222-2-202000-2000000002000000-200000000000000
χ3222-2-222-22-2-2002-22222-2-2-2-200222002-200-2-2-2-2-222-2-22202000-200000000-2000000200000000000000
χ3322-2-222-22-2-2002-22-12-1-2-21100-12-1−i3i3-11i3−i311-222-2-2-1-1110-1−i3i301i3−i3000000-1−i3i300001i3−i3000000000000
χ3422-2-222-22-2-2002-22-12-1-2-21100-12-1−i3i3-11i3−i311-2-2-22211-1-10-1−i3i301i3−i30000001i3−i30000-1−i3i3000000000000
χ3522-2-222-22-2-2002-22-12-1-2-21100-12-1i3−i3-11−i3i311-222-2-2-1-1110-1i3−i301−i3i3000000-1i3−i300001−i3i3000000000000
χ3622-2-222-22-2-2002-22-12-1-2-21100-12-1i3−i3-11−i3i311-2-2-22211-1-10-1i3−i301−i3i30000001−i3i30000-1i3−i3000000000000
χ3722-2-2-2222-2-22-2-222-12-1-2-2112-2-1-21-1-1-1-1111122-22-2-1-11121-1-1-2-111200-2001-1-10000-111000000000000
χ3822-2-2-2222-2-22-2-222-12-1-2-2112-2-1-21-1-1-1-111112-22-2211-1-121-1-1-2-111-200200-11100001-1-1000000000000
χ3922-2-2-2222-2-22-2-22-12-1211-2-22-2-11-222-12-2-211-100000000-11-1-11-11100200-200000-22000000011-1-10-101
χ4022-2-2-2222-2-22-2-22-12-1211-2-22-2-11-222-12-2-211-100000000-11-1-11-11100-2002000002-20000000-1-111010-1
χ4122-2-2-2222-2-2-22-222-12-1-2-211-22-1-2111-1-1-1-11122-22-2-1-111-21112-1-1-1-2002001110000-1-1-1000000000000
χ4222-2-2-2222-2-2-22-222-12-1-2-211-22-1-2111-1-1-1-1112-22-2211-1-1-21112-1-1-1200-200-1-1-10000111000000000000
χ4322-2-2-2222-2-2-22-22-12-1211-2-2-22-11-2-2-2-122211-1000000001111-1-1-1-100200-2000002-20000000-1-1110-101
χ4422-2-2-2222-2-2-22-22-12-1211-2-2-22-11-2-2-2-122211-1000000001111-1-1-1-100-200200000-22000000011-1-1010-1
χ4544444444444444-2-2-2-2-2-2-2-2441-2-2-2-21-2-2-211-200000000-2111-21110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-41-2-2221-22211-20000000021-1-121-1-10000000000000000000000000000
χ474444-44-444400-4-4-24-24-2-24400-22-400-2-400-2-2200000000020002000000000000000000000000000000
χ484444-44-444400-4-4-2-2-2-2-2-2-2-200122−2i32i312−2i32i3112000000000-1i3−i30-1i3−i30000000000000000000000000000
χ494444-44-444400-4-4-2-2-2-2-2-2-2-2001222i3−2i3122i3−2i3112000000000-1−i3i30-1−i3i30000000000000000000000000000
χ5044-4-444-44-4-4004-4-24-2422-4-400-2-2400-2-400222000000000-20002000000000000000000000000000000
χ5144-4-444-44-4-4004-4-2-2-2-22222001-2-2−2i32i3122i3−2i3-1-120000000001i3−i30-1−i3i30000000000000000000000000000
χ5244-4-444-44-4-4004-4-2-2-2-22222001-2-22i3−2i312−2i32i3-1-120000000001−i3i30-1i3−i30000000000000000000000000000
χ5344-4-4-4444-4-44-4-44-2-2-2-222224-4122-2-21-222-1-1-200000000-2-11121-1-10000000000000000000000000000
χ5444-4-4-4444-4-4-44-44-2-2-2-22222-44122221-2-2-2-1-1-2000000002-1-1-1-21110000000000000000000000000000
χ554-44i−4i040-44i−4i000044-4-44i−4i4i−4i0040000-40004i−4i000000000000000000000000000000000000000000000
χ564-44i−4i040-44i−4i00004-2-424i−4i−2i2i00-200002000−2i2i00000−2i32i323−23000000000000000000000000000000000000
χ574-44i−4i040-44i−4i00004-2-424i−4i−2i2i00-200002000−2i2i000002i3−2i3−2323000000000000000000000000000000000000
χ584-44i−4i040-44i−4i0000-242-4−2i2i4i−4i00-200002000−2i2i00000000000000000000000000000000000006−6i6−i60000
χ594-44i−4i040-44i−4i0000-242-4−2i2i4i−4i00-200002000−2i2i0000000000000000000000000000000000000−66−i6i60000
χ604-4−4i4i040-4−4i4i000044-4-4−4i4i−4i4i0040000-4000−4i4i000000000000000000000000000000000000000000000
χ614-4−4i4i040-4−4i4i00004-2-42−4i4i2i−2i00-2000020002i−2i00000−2i32i3−2323000000000000000000000000000000000000
χ624-4−4i4i040-4−4i4i00004-2-42−4i4i2i−2i00-2000020002i−2i000002i3−2i323−23000000000000000000000000000000000000
χ634-4−4i4i040-4−4i4i0000-242-42i−2i−4i4i00-2000020002i−2i00000000000000000000000000000000000006−6−i6i60000
χ644-4−4i4i040-4−4i4i0000-242-42i−2i−4i4i00-2000020002i−2i0000000000000000000000000000000000000−66i6−i60000
χ6566666-36-3-3-366-3-300000000-3-300000000000000000000000000000200200002200000-1-1-1-10000-10-10
χ6666666-36-3-3-366-3-300000000-3-300000000000000000000000000000-200-20000-2-200000111100001010
χ6766666-36-3-3-3-6-6-3-300000000330000000000000000000000000000020020000-2-20000011110000-10-10
χ6866666-36-3-3-3-6-6-3-3000000003300000000000000000000000000000-200-200002200000-1-1-1-100001010
χ6966-6-6-6-36-3336-63-300000000-3300000000000000000000000000000200-200002-200000-1-1110000-1010
χ7066-6-6-6-36-3336-63-300000000-3300000000000000000000000000000-20020000-220000011-1-1000010-10
χ7166-6-6-6-36-333-663-3000000003-300000000000000000000000000000200-20000-220000011-1-10000-1010
χ7266-6-6-6-36-333-663-3000000003-300000000000000000000000000000-200200002-200000-1-111000010-10
χ738-88i−8i080-88i−8i0000-4-444−4i4i−4i4i0020000-20002i−2i000000000000000000000000000000000000000000000
χ748-8−8i8i080-8−8i8i0000-4-4444i−4i4i−4i0020000-2000−2i2i000000000000000000000000000000000000000000000
χ7512121212-12-6-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-1212-6-12-66600-66000000000000000000000000000000000000000000000000000000000000000000
χ7712-1212i−12i0-606−6i6i0000000000000000000000000000000000000000000000000000000000i6−i66−600000000
χ7812-1212i−12i0-606−6i6i0000000000000000000000000000000000000000000000000000000000−i6i6−6600000000
χ7912-12−12i12i0-6066i−6i0000000000000000000000000000000000000000000000000000000000i6−i6−6600000000
χ8012-12−12i12i0-6066i−6i0000000000000000000000000000000000000000000000000000000000−i6i66−600000000

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