Finite Group Databasebeta

← Group #13136708

Character table — Group #13136708

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111122222244999912121212121212121212121218181818181818181818181818182424363636363636363636363636363636363636363636363636363672727272
order12442346121261222443366661212121212122466888888881212612688888888122424242424242424242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111-11-1111-1-1-1-1-1-111-1-1111111-1-111-1-1iiii−i−i−i−i-1-1-1-1111-1-1ii−i−i1iiii−i−i−i−iiiii−i−i−i−i11-1-1
χ61111-11-1111-1-1-1-1-1-111-1-1111111-1-111-1-1iiii−i−i−i−i-1-1-1-11-1-111−i−iii1iiii−i−i−i−i−i−i−i−iiiii-1-111
χ71111-11-1111-1-1-1-1-1-111-1-1111111-1-111-1-1−i−i−i−iiiii-1-1-1-1111-1-1−i−iii1−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ81111-11-1111-1-1-1-1-1-111-1-1111111-1-111-1-1−i−i−i−iiiii-1-1-1-11-1-111ii−i−i1−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ911-1-111-11-1-11-1-1-111111111-1-1-1-1-1-1-11-1-1ii−i−iii−i−i111-1-1i−ii−i1-11-11ii−i−iii−i−i11-1-111-1-1i−ii−i
χ1011-1-111-11-1-11-1-1-111111111-1-1-1-1-1-1-11-1-1ii−i−iii−i−i111-1-1−ii−ii-11-111ii−i−iii−i−i-1-111-1-111−ii−ii
χ1111-1-111-11-1-11-1-1-111111111-1-1-1-1-1-1-11-1-1−i−iii−i−iii111-1-1i−ii−i-11-111−i−iii−i−iii-1-111-1-111i−ii−i
χ1211-1-111-11-1-11-1-1-111111111-1-1-1-1-1-1-11-1-1−i−iii−i−iii111-1-1−ii−ii1-11-11−i−iii−i−iii11-1-111-1-1−ii−ii
χ1311-1-1-1111-1-1-1111-1-111-1-111-1-1-1-111-111111-1-1-1-111-1-1-11-1i−i−ii−iii−i111-1-1-1-111−i−iiiii−i−ii−i−ii
χ1411-1-1-1111-1-1-1111-1-111-1-111-1-1-1-111-111111-1-1-1-111-1-1-11-1−iii−ii−i−ii111-1-1-1-111ii−i−i−i−iii−iii−i
χ1511-1-1-1111-1-1-1111-1-111-1-111-1-1-1-111-1111-1-11111-1-1-1-1-11-1i−i−iii−i−ii1-1-11111-1-1ii−i−i−i−iiii−i−ii
χ1611-1-1-1111-1-1-1111-1-111-1-111-1-1-1-111-1111-1-11111-1-1-1-1-11-1−iii−i−iii−i1-1-11111-1-1−i−iiiii−i−i−iii−i
χ17222222222222-2-2-2-2222222222222-2-2-2-200000000-2-222-200000000-200000000000000000000
χ182222-22-2222-2-2222222-2-2222222-2-2-2-2220000000022-2-2-200000000-200000000000000000000
χ1922-2-222-22-2-22-222-2-2222222-2-2-2-2-2-22-22200000000-2-22-2200000000-200000000000000000000
χ2022-2-2-2222-2-2-22-2-22222-2-222-2-2-2-2222-2-2-20000000022-22200000000-200000000000000000000
χ212-22i−2i020-22i−2i002-22i−2i2200-2-22i−2i2i−2i00002-22−2−i2i2−i2i22−22i−2i0000000000002−2−i2i2−i2i22−2000000000000
χ222-22i−2i020-22i−2i002-22i−2i2200-2-22i−2i2i−2i00002-2−22i2−i2i2−i2−222i−2i000000000000−22i2−i2i2−i2−22000000000000
χ232-22i−2i020-22i−2i00-22−2i2i2200-2-22i−2i2i−2i0000-22−i2i2−222−2i2−i2−2i2i000000000000−i2i2−222−2i2−i2000000000000
χ242-22i−2i020-22i−2i00-22−2i2i2200-2-22i−2i2i−2i0000-22i2−i22−2−22−i2i2−2i2i000000000000i2−i22−2−22−i2i2000000000000
χ252-2−2i2i020-2−2i2i002-2−2i2i2200-2-2−2i2i−2i2i00002-22−2i2−i2i2−i22−2−2i2i0000000000002−2i2−i2i2−i22−2000000000000
χ262-2−2i2i020-2−2i2i002-2−2i2i2200-2-2−2i2i−2i2i00002-2−22−i2i2−i2i2−22−2i2i000000000000−22−i2i2−i2i2−22000000000000
χ272-2−2i2i020-2−2i2i00-222i−2i2200-2-2−2i2i−2i2i0000-22−i2i22−2−22i2−i22i−2i000000000000−i2i22−2−22i2−i2000000000000
χ282-2−2i2i020-2−2i2i00-222i−2i2200-2-2−2i2i−2i2i0000-22i2−i2−222−2−i2i22i−2i000000000000i2−i2−222−2−i2i2000000000000
χ2944444444444400001-2111-211-2-21100002222222200-2-20000000000-1-1-1-1-1-1-1-1000000000000
χ3044444444444400001-2111-211-2-2110000-2-2-2-2-2-2-2-200-2-2000000000011111111000000000000
χ314444444444440000-21-2-2-21-2-211-2-2000000000000001102222000000000000000000000-1-1-1-1
χ324444444444440000-21-2-2-21-2-211-2-200000000000000110-2-2-2-20000000000000000000001111
χ334444-44-4444-4-400001-2-1-11-211-2-2-1-100002i2i2i2i−2i−2i−2i−2i00220000000000−i−i−i−iiiii000000000000
χ344444-44-4444-4-400001-2-1-11-211-2-2-1-10000−2i−2i−2i−2i2i2i2i2i00220000000000iiii−i−i−i−i000000000000
χ354444-44-4444-4-40000-2122-21-2-2112200000000000000-1-1022-2-2000000000000000000000-1-111
χ364444-44-4444-4-40000-2122-21-2-2112200000000000000-1-10-2-22200000000000000000000011-1-1
χ3744-4-444-44-4-44-400001-2111-2-1-122-1-100002i2i−2i−2i2i2i−2i−2i00-220000000000−i−iii−i−iii000000000000
χ3844-4-444-44-4-44-400001-2111-2-1-122-1-10000−2i−2i2i2i−2i−2i2i2i00-220000000000ii−i−iii−i−i000000000000
χ3944-4-444-44-4-44-40000-21-2-2-2122-1-122000000000000001-102i−2i2i−2i000000000000000000000−ii−ii
χ4044-4-444-44-4-44-40000-21-2-2-2122-1-122000000000000001-10−2i2i−2i2i000000000000000000000i−ii−i
χ4144-4-4-4444-4-4-4400001-2-1-11-2-1-12211000022-2-2-2-222002-20000000000-1-11111-1-1000000000000
χ4244-4-4-4444-4-4-4400001-2-1-11-2-1-122110000-2-22222-2-2002-2000000000011-1-1-1-111000000000000
χ4344-4-4-4444-4-4-440000-2122-2122-1-1-2-200000000000000-1102i−2i−2i2i000000000000000000000−iii−i
χ4444-4-4-4444-4-4-440000-2122-2122-1-1-2-200000000000000-110−2i2i2i−2i000000000000000000000i−i−ii
χ454-44i−4i040-44i−4i0000001-23-3-12i−i−2i2i3i−3i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13000000000000
χ464-44i−4i040-44i−4i0000001-23-3-12i−i−2i2i3i−3i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13000000000000
χ474-44i−4i040-44i−4i0000001-2-33-12i−i−2i2i−3i3i0000−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23000000000000
χ484-44i−4i040-44i−4i0000001-2-33-12i−i−2i2i−3i3i00002ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23000000000000
χ494-4−4i4i040-4−4i4i0000001-23-3-12−ii2i−2i−3i3i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23000000000000
χ504-4−4i4i040-4−4i4i0000001-23-3-12−ii2i−2i−3i3i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23000000000000
χ514-4−4i4i040-4−4i4i0000001-2-33-12−ii2i−2i3i−3i00002ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13000000000000
χ524-4−4i4i040-4−4i4i0000001-2-33-12−ii2i−2i3i−3i0000−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13000000000000
χ5366666-36-3-3-3-3-3222200000000000022-1-100000000-1-100-100000000-1000000003−33−33−33−30000
χ5466666-36-3-3-3-3-3222200000000000022-1-100000000-1-100-100000000-100000000−33−33−33−330000
χ5566666-36-3-3-3-3-3-2-2-2-2000000000000-2-211000000001100100002222100000000-1-1-1-1-1-1-1-10000
χ5666666-36-3-3-3-3-3-2-2-2-2000000000000-2-21100000000110010000-2-2-2-2100000000111111110000
χ576666-6-3-6-3-3-3332222000000000000-2-2-1-100000000-1-100100002i2i−2i−2i100000000−i−i−i−iiiii0000
χ586666-6-3-6-3-3-3332222000000000000-2-2-1-100000000-1-10010000−2i−2i2i2i100000000iiii−i−i−i−i0000
χ596666-6-3-6-3-3-333-2-2-2-20000000000002211000000001100-100000000-100000000−i3i3−i3i3i3−i3i3−i30000
χ606666-6-3-6-3-3-333-2-2-2-20000000000002211000000001100-100000000-100000000i3−i3i3−i3−i3i3−i3i30000
χ6166-6-66-3-6-333-3322-2-20000000000002-2-1-1000000001100-100002-22-2100000000-1-111-1-1110000
χ6266-6-66-3-6-333-3322-2-20000000000002-2-1-1000000001100-10000-22-2210000000011-1-111-1-10000
χ6366-6-66-3-6-333-33-2-222000000000000-221100000000-1-100100000000-1000000003−3−333−3−330000
χ6466-6-66-3-6-333-33-2-222000000000000-221100000000-1-100100000000-100000000−333−3−333−30000
χ6566-6-6-6-36-3333-322-2-2000000000000-22-1-1000000001100100000000-100000000−i3i3i3−i3i3−i3−i3i30000
χ6666-6-6-6-36-3333-322-2-2000000000000-22-1-1000000001100100000000-100000000i3−i3−i3i3−i3i3i3−i30000
χ6766-6-6-6-36-3333-3-2-2220000000000002-21100000000-1-100-100002i−2i−2i2i100000000−i−iiiii−i−i0000
χ6866-6-6-6-36-3333-3-2-2220000000000002-21100000000-1-100-10000−2i2i2i−2i100000000ii−i−i−i−iii0000
χ698-88i−8i080-88i−8i000000-42004-2−4i4i2i−2i000000000000000000000000000000000000000000000000
χ708-8−8i8i080-8−8i8i000000-42004-24i−4i−2i2i000000000000000000000000000000000000000000000000
χ7112-1212i−12i0-606−6i6i004-44i−4i00000000000000-2200000000−2i2i00000000000000000000000000000000
χ7212-1212i−12i0-606−6i6i00-44−4i4i000000000000002-2000000002i−2i00000000000000000000000000000000
χ7312-12−12i12i0-6066i−6i004-4−4i4i00000000000000-22000000002i−2i00000000000000000000000000000000
χ7412-12−12i12i0-6066i−6i00-444i−4i000000000000002-200000000−2i2i00000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.