Finite Group Databasebeta

← Group #13180193

Character table — Group #13180193

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size113344448899121212121212181824242424242424242727323232325454727272727272108108108108108108
order12223366362224666644666612121212223366446612121212244444
χ1111111111111111111111111111111111111111111111111
χ2111111111111111111-1-111111111111111-1-111-1-1-1-111-1-1-1-1
χ3111111111111-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ4111111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111
χ51111111111-1-1111111i−i11111111-1-11111i−i-1-1ii−i−i-1-1i−ii−i
χ61111111111-1-1111111−ii11111111-1-11111−ii-1-1−i−iii-1-1−ii−ii
χ71111111111-1-1-1-11111i−i-1-1-1-1-1-1-1-1-1-11111i−i-1-1ii−i−i11−ii−ii
χ81111111111-1-1-1-11111−ii-1-1-1-1-1-1-1-1-1-11111−ii-1-1−i−iii11i−ii−i
χ922222222-1-122002222220000000022-1-1-1-122-1-1-1-1-1-1000000
χ1022222222-1-122002222-2-20000000022-1-1-1-1-2-2-1-11111000000
χ1122222222-1-1-2-20022222i−2i00000000-2-2-1-1-1-12i−2i11−i−iii000000
χ1222222222-1-1-2-2002222−2i2i00000000-2-2-1-1-1-1−2i2i11ii−i−i000000
χ132-2-2222-2-22-22-200-2-22200000000002-222-2-200-220000000000
χ142-2-2222-2-22-2-2200-2-2220000000000-2222-2-2002-20000000000
χ152-2-2222-2-2-112-200-2-22200000000002-2-1-111001-1−i3i3−i3i3000000
χ162-2-2222-2-2-112-200-2-22200000000002-2-1-111001-1i3−i3i3−i3000000
χ172-2-2222-2-2-11-2200-2-2220000000000-22-1-11100-113−3−33000000
χ182-2-2222-2-2-11-2200-2-2220000000000-22-1-11100-11−333−3000000
χ1933-1-1333300331-1-1-1-1-1331111-1-1-1-1-1-10000-1-10000001-111-1-1
χ2033-1-1333300331-1-1-1-1-1-3-31111-1-1-1-1-1-10000110000001-1-1-111
χ2133-1-133330033-11-1-1-1-133-1-1-1-11111-1-10000-1-1000000-11-1-111
χ2233-1-133330033-11-1-1-1-1-3-3-1-1-1-11111-1-1000011000000-1111-1-1
χ2333-1-1333300-3-31-1-1-1-1-13i−3i1111-1-1-1-1110000−ii000000-11i−i−ii
χ2433-1-1333300-3-31-1-1-1-1-1−3i3i1111-1-1-1-1110000i−i000000-11−iii−i
χ2533-1-1333300-3-3-11-1-1-1-13i−3i-1-1-1-11111110000−ii0000001-1−iii−i
χ2633-1-1333300-3-3-11-1-1-1-1−3i3i-1-1-1-11111110000i−i0000001-1i−i−ii
χ2744441-21-24400441-21-20011-2-211-2-2001-21-200000000000000
χ2844441-21-24400-4-41-21-200-1-122-1-122001-21-200000000000000
χ294444-21-21440044-21-2100-2-211-2-21100-21-2100000000000000
χ304444-21-214400-4-4-21-210022-1-122-1-100-21-2100000000000000
χ314-4-441-2-124-40000-121-2003-3003-300001-2-1200000000000000
χ324-4-441-2-124-40000-121-200-3300-3300001-2-1200000000000000
χ334-4-44-212-14-400002-1-2100003-3003-300-212-100000000000000
χ344-4-44-212-14-400002-1-210000-3300-3300-212-100000000000000
χ356-62-266-6-6006-60022-2-20000000000-22000000000000000000
χ366-62-266-6-600-660022-2-200000000002-2000000000000000000
χ3788882-42-4-4-400002-42-4000000000000-12-1200000000000000
χ388888-42-42-4-40000-42-420000000000002-12-100000000000000
χ398-8-882-4-24-440000-242-4000000000000-121-200000000000000
χ408-8-88-424-2-4400004-2-420000000000002-1-2100000000000000
χ411212-4-43-63-600004-4-12-120011-2-2-1-12200000000000000000000
χ421212-4-43-63-60000-44-12-1200-1-12211-2-200000000000000000000
χ431212-4-4-63-6300004-42-12-100-2-21122-1-100000000000000000000
χ441212-4-4-63-630000-442-12-10022-1-1-2-21100000000000000000000
χ4512-124-43-6-360000001-2-12003-300-330000000000000000000000
χ4612-124-43-6-360000001-2-1200-33003-30000000000000000000000
χ4712-124-4-636-3000000-212-100003-300-3300000000000000000000
χ4812-124-4-636-3000000-212-10000-33003-300000000000000000000

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