Finite Group Databasebeta

← Group #13148658

Character table — Group #13148658

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order12223446662412123366666661236666612121212121244441212121266612121212122222444444666612121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-11-11-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-1-11-11
χ51111111111-1-11111111111-1-11-1-11111111-1-111111111-1-1-1-111-1-11-11-1-1-11-11-111111111-1-111-1-1-1-1-1-1
χ61111111111-1-11111111111-1-11-1-11111111-1-111111111-1-1-1-111-1-1-11-11-1-1-11-11-1-1-1-1-1-111-1-1-1-1-1-11111
χ71111111111-1-11111111111-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11111-1-1111-1-111-1-111-1-111-11-11
χ81111111111-1-11111111111-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-111-111-1-1-111-1-1-1-11111111-11-1
χ911111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-111-1-11111111-1-1-1-1-11-11-11-1-11-111111-1-1-1-1-1-1-1-111-1-111
χ1011111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-111-1-11111111-1-1-1-1-1-11-111-11-11-1-1-1-1-111-1-1-1-1111111-1-1
χ1111111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-11-1-11-11-111-111-1-1-1-1111111-1-1-111-1
χ1211111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-111-1-111-1-11-1-111111111-1-1-1-11-1-11
χ1311111-1-1111-11-1-111111111-111-1-1111-1-1-1-11111-1-11111-1-1-11-1-1111111-11-1-1-1-11111-1-1-1-111-1-1-1-111-1-1
χ1411111-1-1111-11-1-111111111-111-1-1111-1-1-1-11111-1-11111-1-1-11-1-111-1-1-1-1-111111-1-1-1-111-1-11111-1-1-1-111
χ1511111-1-1111-11-1-111111111-111-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-11-1-11111-1-11-1-1-11111-1-1-1-111-1-111111-1-11
χ1611111-1-1111-11-1-111111111-111-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-11-1-111-1-1111-111-1-1-1-1111111-1-1-1-111-111-1
χ17222222222222222-1-122-1-1222-122-1-1-122-1-12200000000-1-1-1-1-1-1-1-1002200002200-1-1000000-1-1000-10-1
χ18222222222222222-1-122-1-1222-122-1-1-122-1-12200000000-1-1-1-1-1-1-1-100-2-20000-2-2001100000011000101
χ1922222222222222-122-1-122-122-1-1-1-1-1-1-1-122-1-12222-1-1-1-12-1-12-1-1-1-10000220000000000-1-1-1-100-1-10000
χ2022222222222222-122-1-122-122-1-1-1-1-1-1-1-122-1-1-2-2-2-211112-1-12-1-1-1-10000-2-20000000000111100110000
χ212222222222-2-2222-1-122-1-12-2-2-1-2-2-1-1-122-1-1-2-2000000001111-1-111002-200002-200-1-1000000-1-1000101
χ222222222222-2-2222-1-122-1-12-2-2-1-2-2-1-1-122-1-1-2-2000000001111-1-11100-220000-22001100000011000-10-1
χ232222222222-2-222-122-1-122-1-2-2-111-1-1-1-1-122112222-1-1-1-1-211-2-1-1110000-2-20000000000-1-11100110000
χ242222222222-2-222-122-1-122-1-2-2-111-1-1-1-1-12211-2-2-2-21111-211-2-1-111000022000000000011-1-100-1-10000
χ2522222-2-22222-2-2-22-1-122-1-122-2-122-1-1-1-2-211-2-200000000-1-1-111111002-20000-2200-1-10000001100010-1
χ2622222-2-22222-2-2-22-1-122-1-122-2-122-1-1-1-2-211-2-200000000-1-1-11111100-2200002-20011000000-1-1000-101
χ2722222-2-22222-2-2-2-122-1-122-12-2-1-1-1-1-1-111-2-21122-2-2-1-1-1-12-1-1-2111100002-20000000000111100-1-10000
χ2822222-2-22222-2-2-2-122-1-122-12-2-1-1-1-1-1-111-2-211-2-22211112-1-1-211110000-220000000000-1-1-1-100110000
χ2922222-2-2222-22-2-22-1-122-1-12-22-1-2-2-1-1-1-2-2112200000000111-111-1-100220000-2-200-1-100000011000-101
χ3022222-2-2222-22-2-22-1-122-1-12-22-1-2-2-1-1-1-2-2112200000000111-111-1-100-2-20000220011000000-1-100010-1
χ3122222-2-2222-22-2-2-122-1-122-1-22-111-1-1-111-2-2-1-122-2-2-1-1-1-1-211211-1-10000-22000000000011-1-100110000
χ3222222-2-2222-22-2-2-122-1-122-1-22-111-1-1-111-2-2-1-1-2-2221111-211211-1-100002-20000000000-1-11100-1-10000
χ3322-2-222i−2i2-2-2002i−2i222-2-2-2-22002002-2-22i−2i2i−2i002-22i−2i22-2-200002i−2i0000000000000000002i−2i0000000000
χ3422-2-222i−2i2-2-2002i−2i222-2-2-2-22002002-2-22i−2i2i−2i00-22−2i2i-2-22200002i−2i000000000000000000−2i2i0000000000
χ3522-2-222i−2i2-2-2002i−2i-12211-2-2-100-1−i3i3-111−ii2i−2i3−32-22i−2i-1-1110−i3i30−ii3−30000000000000000−ii3−300−i3i30000
χ3622-2-222i−2i2-2-2002i−2i-12211-2-2-100-1−i3i3-111−ii2i−2i3−3-22−2i2i11-1-10−i3i30−ii3−30000000000000000i−i−3300i3−i30000
χ3722-2-222i−2i2-2-2002i−2i-12211-2-2-100-1i3−i3-111−ii2i−2i−332-22i−2i-1-1110i3−i30−ii−330000000000000000−ii−3300i3−i30000
χ3822-2-222i−2i2-2-2002i−2i-12211-2-2-100-1i3−i3-111−ii2i−2i−33-22−2i2i11-1-10i3−i30−ii−330000000000000000i−i3−300−i3i30000
χ3922-2-22−2i2i2-2-200−2i2i222-2-2-2-22002002-2-2−2i2i−2i2i002-2−2i2i22-2-20000−2i2i000000000000000000−2i2i0000000000
χ4022-2-22−2i2i2-2-200−2i2i222-2-2-2-22002002-2-2−2i2i−2i2i00-222i−2i-2-2220000−2i2i0000000000000000002i−2i0000000000
χ4122-2-22−2i2i2-2-200−2i2i-12211-2-2-100-1−i3i3-111i−i−2i2i−332-2−2i2i-1-1110−i3i30i−i−330000000000000000i−i−3300−i3i30000
χ4222-2-22−2i2i2-2-200−2i2i-12211-2-2-100-1−i3i3-111i−i−2i2i−33-222i−2i11-1-10−i3i30i−i−330000000000000000−ii3−300i3−i30000
χ4322-2-22−2i2i2-2-200−2i2i-12211-2-2-100-1i3−i3-111i−i−2i2i3−32-2−2i2i-1-1110i3−i30i−i3−30000000000000000i−i3−300i3−i30000
χ4422-2-22−2i2i2-2-200−2i2i-12211-2-2-100-1i3−i3-111i−i−2i2i3−3-222i−2i11-1-10i3−i30i−i3−30000000000000000−ii−3300−i3i30000
χ4544444444444444-2-2-2-2-2-2-2-2441-2-2111-2-2-2-2-2-200000000-211-211110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-4122111-2-2-2-222000000002-1-1211-1-10000000000000000000000000000
χ4744444-4-44444-4-4-4-2-2-2-2-2-2-2-24-41-2-211122222200000000-2112-1-1-1-10000000000000000000000000000
χ4844444-4-4444-44-4-4-2-2-2-2-2-2-2-2-441221112222-2-2000000002-1-1-2-1-1110000000000000000000000000000
χ4944-4-444i−4i4-4-4004i−4i4-2-2-4-422400-200-2224i−4i−2i2i00000000000000−2i2i000000000000000000000000000000
χ5044-4-444i−4i4-4-4004i−4i-2-2-22222-2001−2i32i31-1-1−2i2i−2i2i23−23000000000i3−i30i−i−330000000000000000000000000000
χ5144-4-444i−4i4-4-4004i−4i-2-2-22222-20012i3−2i31-1-1−2i2i−2i2i−2323000000000−i3i30i−i3−30000000000000000000000000000
χ5244-4-44−4i4i4-4-400−4i4i4-2-2-4-422400-200-222−4i4i2i−2i000000000000002i−2i000000000000000000000000000000
χ5344-4-44−4i4i4-4-400−4i4i-2-2-22222-2001−2i32i31-1-12i−2i2i−2i−2323000000000i3−i30−ii3−30000000000000000000000000000
χ5444-4-44−4i4i4-4-400−4i4i-2-2-22222-20012i3−2i31-1-12i−2i2i−2i23−23000000000−i3i30−ii−330000000000000000000000000000
χ554-44-4400-44-4000044-44-44-4-400400-44-400000000000000000000000000000000000000000000000000
χ564-44-4400-44-400004-224-4-22-400-2002-22000000000000000000000000000000000000000000−2i32i3000000
χ574-44-4400-44-400004-224-4-22-400-2002-220000000000000000000000000000000000000000002i3−2i3000000
χ584-44-4400-44-40000-24-4-224-4200-2002-22000000000023−2323−23000000000000000000000000000000000000
χ594-44-4400-44-40000-24-4-224-4200-2002-220000000000−2323−2323000000000000000000000000000000000000
χ604-4-44400-4-44000044-4-44-44-400400-4-4400000000000000000000000000000000000000000000000000
χ614-4-44400-4-4400004-22-442-2-400-20022-20000000000000000000000000000000000−2i32i300000000000000
χ624-4-44400-4-4400004-22-442-2-400-20022-200000000000000000000000000000000002i3−2i300000000000000
χ634-4-44400-4-440000-24-42-2-44200-20022-2000000000023−23−2323000000000000000000000000000000000000
χ644-4-44400-4-440000-24-42-2-44200-20022-20000000000−232323−23000000000000000000000000000000000000
χ656666-366-3-3-366-3-300000000-3-300000000000000000000000000002200002200-1-100-1-100000000-10-10
χ666666-366-3-3-366-3-300000000-3-30000000000000000000000000000-2-20000-2-200110011000000001010
χ676666-366-3-3-3-6-6-3-3000000003300000000000000000000000000002-200002-200-1-100-1-1000000001010
χ686666-366-3-3-3-6-6-3-300000000330000000000000000000000000000-220000-220011001100000000-10-10
χ696666-3-6-6-3-3-36-63300000000-3300000000000000000000000000002-20000-2200-1-100110000000010-10
χ706666-3-6-6-3-3-36-63300000000-330000000000000000000000000000-2200002-2001100-1-100000000-1010
χ716666-3-6-6-3-3-3-6633000000003-30000000000000000000000000000220000-2-200-1-1001100000000-1010
χ726666-3-6-6-3-3-3-6633000000003-30000000000000000000000000000-2-2000022001100-1-10000000010-10
χ738-88-8800-88-80000-4-44-44-44400200-22-200000000000000000000000000000000000000000000000000
χ748-8-88800-8-880000-4-444-44-4400200-2-2200000000000000000000000000000000000000000000000000
χ751212-12-12-612i−12i-66600−6i6i000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-6−12i12i-666006i−6i000000000000000000000000000000000000000000000000000000000000000000
χ7712-1212-12-6006-6600000000000000000000000000000000000000000000000000000000−2i32i3000000000000
χ7812-1212-12-6006-66000000000000000000000000000000000000000000000000000000002i3−2i3000000000000
χ7912-12-1212-60066-60000000000000000000000000000000000000000000000000000−2i32i30000000000000000
χ8012-12-1212-60066-600000000000000000000000000000000000000000000000000002i3−2i30000000000000000

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