Finite Group Databasebeta

← Group #13151945

Character table — Group #13151945

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size112222222444466668812121212121212121212121212121818181818182424242424242424363636363636363636363636363636363636363636727272727272
order1223446121224612336661236666612121212121212122244886666121212122224446688812121212121224242424666122424
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-111111111-1-1-111-111-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-111111111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-111
χ5111111111-1-1111111-1-111-1-111111-1-1111111111-11-1-1-11-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-111
χ6111111111-1-1111111-1-111-1-111111-1-11111111-1-1-11-1-1-11-1-1111-1-1111-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ7111111111-1-1111111-1-111-1-111111-1-1111-1-1-1-111-11-1-1-11-1-1-11111-1-1-11-1-1-1-111111111-111-1-1-1
χ8111111111-1-1111111-1-111-1-111111-1-1111-1-1-1-1-1-1-11-1-1-11-1-11-1-1111-1-1-111-1-11111-1-1-1-11-1-1111
χ911-11-111-1-11-1-1111111-11-111-11-11-1-1-1-1-111-11-1111-111-11-1-1-11-11-111-1-11-11-111-1-111-1-1-11-111-1
χ1011-11-111-1-11-1-1111111-11-111-11-11-1-1-1-1-111-11-1-1-11-111-11-1-11-111-1-11-11-111-111-1-1-1-1111-11-1-11
χ1111-11-111-1-11-1-1111111-11-111-11-11-1-1-1-1-11-11-11111-111-11-1-1-1-11-111-11-1-11-11-1-11111-1-1-1-111-11
χ1211-11-111-1-11-1-1111111-11-111-11-11-1-1-1-1-11-11-11-1-11-111-11-1-111-1-11-1-1111-1-11-1-111-1-11111-1-11-1
χ1311-11-111-1-1-11-111111-111-1-1-1-11-11-111-1-111-11-111-1-1-1-111111-11-11-11-1-11-11-1-1-11111-1-11-11-11-1
χ1411-11-111-1-1-11-111111-111-1-1-1-11-11-111-1-111-11-1-1-1-1-1-1-11111-11-1-1111-11-111-1-1-111-1-111-11-11-11
χ1511-11-111-1-1-11-111111-111-1-1-1-11-11-111-1-11-11-1111-1-1-1-1111111-11-1-1-11-1-11-1111-1-111-1-111-1-1-11
χ1611-11-111-1-1-11-111111-111-1-1-1-11-11-111-1-11-11-11-1-1-1-1-1-11111-1-111-11-1111-1-1111-1-1-1-111-1-1111-1
χ1722222222222222-1-1222-1222-1-1-12222-1-1-1000000-1-1-1-1-1-1-1-10220000002200000000000-1-10-1-1
χ1822222222222222-1-1222-1222-1-1-12222-1-1-1000000-1-1-1-1-1-1-1-10-2-2000000-2-20000000000011011
χ192222222222222-122-122-1-1-1-12-12-1-1-1-1-1-122222002-1-1-12-1-1-1000220-1-1000-1-1-1-1-1-10000000000
χ202222222222222-122-122-1-1-1-12-12-1-1-1-1-1-12-2-2-2-2002-1-1-12-1-1-1000-2-20110001111110000000000
χ21222222222-2-2222-1-12-2-2-12-2-2-1-1-122-2-2-1-1-10000001-1111-111022000000-2-200000000000-1-1011
χ22222222222-2-2222-1-12-2-2-12-2-2-1-1-122-2-2-1-1-10000001-1111-1110-2-20000002200000000000110-1-1
χ23222222222-2-222-122-1-2-2-1-1112-12-1-111-1-12222200-2-111-2-111000-2-20-1-1000-1-111110000000000
χ24222222222-2-222-122-1-2-2-1-1112-12-1-111-1-12-2-2-2-200-2-111-2-1110002201100011-1-1-1-10000000000
χ252222-2-22-2-2002-2222200220022-2-2-200-2-2-22-2-220002000-2000000002-2000-2200000000000000
χ262222-2-22-2-2002-2222200220022-2-2-200-2-2-2-222-20002000-200000000-220002-200000000000000
χ272222-2-22-2-2002-2-122-100-1-1−i3i32-1-211−i3i311-22-2-22000-1−i3i301−i3i3000000-110001-1−i3i3−i3i30000000000
χ282222-2-22-2-2002-2-122-100-1-1−i3i32-1-211−i3i311-2-222-2000-1−i3i301−i3i30000001-1000-11i3−i3i3−i30000000000
χ292222-2-22-2-2002-2-122-100-1-1i3−i32-1-211i3−i311-22-2-22000-1i3−i301i3−i3000000-110001-1i3−i3i3−i30000000000
χ302222-2-22-2-2002-2-122-100-1-1i3−i32-1-211i3−i311-2-222-2000-1i3−i301i3−i30000001-1000-11−i3i3−i3i30000000000
χ3122-222-222200-2-22222002-200-222-220022-222-2-2000-2000-20000000022000-2-200000000000000
χ3222-222-222200-2-22222002-200-222-220022-2-2-222000-2000-200000000-2-20002200000000000000
χ3322-222-222200-2-2-122-100-11−i3i3-2-121-1i3−i3-1-1-222-2-20001−i3i301i3−i3000000-1-100011−i3i3i3−i30000000000
χ3422-222-222200-2-2-122-100-11−i3i3-2-121-1i3−i3-1-1-2-2-2220001−i3i301i3−i300000011000-1-1i3−i3−i3i30000000000
χ3522-222-222200-2-2-122-100-11i3−i3-2-121-1−i3i3-1-1-222-2-20001i3−i301−i3i3000000-1-100011i3−i3−i3i30000000000
χ3622-222-222200-2-2-122-100-11i3−i3-2-121-1−i3i3-1-1-2-2-2220001i3−i301−i3i300000011000-1-1−i3i3i3−i30000000000
χ3722-22-222-2-22-2-222-1-122-2-1-2221-112-2-2-211-1000000-11-1-11-11102-20000002-200000000000-110-11
χ3822-22-222-2-22-2-222-1-122-2-1-2221-112-2-2-211-1000000-11-1-11-1110-22000000-22000000000001-101-1
χ3922-22-222-2-22-2-22-122-12-2-11-1-1-2-1-2-11111122-22-20021-1-1-2-1110002-20-11000-11-1-1110000000000
χ4022-22-222-2-22-2-22-122-12-2-11-1-1-2-1-2-1111112-22-220021-1-1-2-111000-2201-10001-111-1-10000000000
χ4122-22-222-2-2-22-222-1-12-22-1-2-2-21-112-22211-10000001111-1-1-1-102-2000000-2200000000000-1101-1
χ4222-22-222-2-2-22-222-1-12-22-1-2-2-21-112-22211-10000001111-1-1-1-10-220000002-2000000000001-10-11
χ4322-22-222-2-2-22-22-122-1-22-1111-2-1-2-11-1-11122-22-200-21112-1-1-1000-220-11000-1111-1-10000000000
χ4422-22-222-2-2-22-22-122-1-22-1111-2-1-2-11-1-1112-22-2200-21112-1-1-10002-201-10001-1-1-1110000000000
χ454444444444444-2-2-2-2441-2-2-2-21-2-2-2-2-211-2000000-2111-2111000000000000000000000000000
χ46444444444-4-444-2-2-2-2-4-41-222-21-2-2-22211-200000021-1-121-1-1000000000000000000000000000
χ474444-4-44-4-4004-44-2-2400-2400-2-22-4-4002220000000-2000200000000000000000000000000000
χ484444-4-44-4-4004-4-2-2-2-2001-2−2i32i3-21222−2i32i3-1-1200000001i3−i30-1i3−i3000000000000000000000000000
χ494444-4-44-4-4004-4-2-2-2-2001-22i3−2i3-212222i3−2i3-1-1200000001−i3i30-1−i3i3000000000000000000000000000
χ5044-444-444400-4-44-2-2400-2-4002-2-2-4400-2-2200000002000200000000000000000000000000000
χ5144-444-444400-4-4-2-2-2-20012−2i32i321-22-22i3−2i31120000000-1i3−i30-1−i3i3000000000000000000000000000
χ5244-444-444400-4-4-2-2-2-200122i3−2i321-22-2−2i32i31120000000-1−i3i30-1i3−i3000000000000000000000000000
χ5344-44-444-4-44-4-44-2-2-2-24-412-2-2212-2222-1-1-2000000-2-11121-1-1000000000000000000000000000
χ5444-44-444-4-4-44-44-2-2-2-2-441222212-22-2-2-1-1-20000002-1-1-1-2111000000000000000000000000000
χ554-40400-400000044-4-40040000-4000000000000−2i22i20000000000000000000000000−2i22i200000000
χ564-40400-400000044-4-40040000-40000000000002i2−2i200000000000000000000000002i2−2i200000000
χ57666-366-3-3-366-3-30000-3-3000000000000000000220000000020000200200000000-1-1-1-1-100-100
χ58666-366-3-3-366-3-30000-3-3000000000000000000-2-200000000-20000-200-2000000001111100100
χ59666-366-3-3-3-6-6-3-30000330000000000000000002200000000-20000-200200000000-1-1-1-1100100
χ60666-366-3-3-3-6-6-3-3000033000000000000000000-2-20000000020000200-2000000001111-100-100
χ6166-6-3-66-3336-63-30000-330000000000000000002200000000-20000200-200000000-1-111100-100
χ6266-6-3-66-3336-63-30000-33000000000000000000-2-20000000020000-20020000000011-1-1-100100
χ6366-6-3-66-333-663-300003-3000000000000000000220000000020000-200-200000000-1-111-100100
χ6466-6-3-66-333-663-300003-3000000000000000000-2-200000000-2000020020000000011-1-1100-100
χ658-80800-80000008-44-800-4000040000000000000000000000000000000000000000000000000
χ668-80800-8000000-48-8400-4000040000000000000000000000000000000000000000000000000
χ678-80800-8000000-4-4440020000-2000006i−6i000000000000000000000000000000000000000000
χ688-80800-8000000-4-4440020000-200000−6i6i000000000000000000000000000000000000000000
χ69121212-6-12-12-66600-660000000000000000000000000000000000000000000000000000000000000
χ701212-12-612-12-6-6-600660000000000000000000000000000000000000000000000000000000000000
χ7112-120-600663−630000000000000000000000000000−2i22i20000000000000000000000000i2−i2i6−i6000000
χ7212-120-600663−6300000000000000000000000000002i2−2i20000000000000000000000000−i2i2−i6i6000000
χ7312-120-6006−63630000000000000000000000000000−2i22i20000000000000000000000000i2−i2−i6i6000000
χ7412-120-6006−636300000000000000000000000000002i2−2i20000000000000000000000000−i2i2i6−i6000000

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