Finite Group Databasebeta

← Group #13146681

Character table — Group #13146681

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size112224991212121212121818181818181824363636363636363636363636367272112224991212121212121818181818181824363636363636363636363636367272
order12236644336666444441212624881212121212242424246122226664466666644444121262488121212121224242424612
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-111111-1-1-1-1-1-11111111111111111111111-1-1-1-111111-1-1-1-1-1-1
χ3111111111111111-1-1-1-111111-1-11-1-1-1-1-1-1-1-111111111111111111-1-1-1-111111-1-11-1-1-1-1-1-1-1-111
χ4111111111111111-1-1-1-1111-1-1111-1-1-1-11111-1-1111111111111111-1-1-1-1111-1-1111-1-1-1-11111-1-1
χ511-111-1-1-1111-11-11ii−i−i-1-1-11-1i−i1ii−i−iii−i−i1-111-111-1-1-1111-11-11ii−i−i-1-1-11-1i−i1ii−i−iii−i−i1-1
χ611-111-1-1-1111-11-11ii−i−i-1-1-1-11−ii1ii−i−i−i−iii-1111-111-1-1-1111-11-11ii−i−i-1-1-1-11−ii1ii−i−i−i−iii-11
χ711-111-1-1-1111-11-11−i−iii-1-1-11-1−ii1−i−iii−i−iii1-111-111-1-1-1111-11-11−i−iii-1-1-11-1−ii1−i−iii−i−iii1-1
χ811-111-1-1-1111-11-11−i−iii-1-1-1-11i−i1−i−iiiii−i−i-1111-111-1-1-1111-11-11−i−iii-1-1-1-11i−i1−i−iiiii−i−i-11
χ9222222-2-2222222-20000-2-220000-20000000000222222-2-2222222-20000-2-220000-20000000000
χ1022-222-222222-22-2-2000022-20000-2000000000022-222-222222-22-2-2000022-20000-20000000000
χ112-202-202i−2i22-20-2001+i−1−i1−i−1+i2i−2i0000001+i−1−i1−i−1+i0000002-202-202i−2i22-20-2001+i−1−i1−i−1+i2i−2i0000001+i−1−i1−i−1+i000000
χ122-202-202i−2i22-20-200−1−i1+i−1+i1−i2i−2i000000−1−i1+i−1+i1−i0000002-202-202i−2i22-20-200−1−i1+i−1+i1−i2i−2i000000−1−i1+i−1+i1−i000000
χ132-202-20−2i2i22-20-2001−i−1+i1+i−1−i−2i2i0000001−i−1+i1+i−1−i0000002-202-20−2i2i22-20-2001−i−1+i1+i−1−i−2i2i0000001−i−1+i1+i−1−i000000
χ142-202-20−2i2i22-20-200−1+i1−i−1−i1+i−2i2i000000−1+i1−i−1−i1+i0000002-202-20−2i2i22-20-200−1+i1−i−1−i1+i−2i2i000000−1+i1−i−1−i1+i000000
χ15444444001-211-210222200-200000-1-1-1-1000000444444001-211-210222200-200000-1-1-1-1000000
χ16444444001-211-210-2-2-2-200-2000001111000000444444001-211-210-2-2-2-200-2000001111000000
χ1744444400-21-2-21-2000000012200000000000-1-144444400-21-2-21-2000000012200000000000-1-1
χ1844444400-21-2-21-200000001-2-2000000000001144444400-21-2-21-200000001-2-20000000000011
χ1944-444-4001-21-1-2-102i2i−2i−2i00200000−i−iii00000044-444-4001-21-1-2-102i2i−2i−2i00200000−i−iii000000
χ2044-444-4001-21-1-2-10−2i−2i2i2i00200000ii−i−i00000044-444-4001-21-1-2-10−2i−2i2i2i00200000ii−i−i000000
χ2144-444-400-21-22120000000-12-200000000000-1144-444-400-21-22120000000-12-200000000000-11
χ2244-444-400-21-22120000000-1-22000000000001-144-444-400-21-22120000000-1-22000000000001-1
χ234-404-40001-2-132-302-22-200000000-11-110000004-404-40001-2-132-302-22-200000000-11-11000000
χ244-404-40001-2-132-30-22-22000000001-11-10000004-404-40001-2-132-30-22-22000000001-11-1000000
χ254-404-40001-2-1-32302i−2i−2i2i00000000−iii−i0000004-404-40001-2-1-32302i−2i−2i2i00000000−iii−i000000
χ264-404-40001-2-1-3230−2i2i2i−2i00000000i−i−ii0000004-404-40001-2-1-3230−2i2i2i−2i00000000i−i−ii000000
χ27666-3-3-32200000020000-1-100000-100003−33−300666-3-3-32200000020000-1-100000-100003−33−300
χ28666-3-3-32200000020000-1-100000-10000−33−3300666-3-3-32200000020000-1-100000-10000−33−3300
χ29666-3-3-3-2-2000000-20000110002210000-1-1-1-100666-3-3-3-2-2000000-20000110002210000-1-1-1-100
χ30666-3-3-3-2-2000000-2000011000-2-210000111100666-3-3-3-2-2000000-2000011000-2-210000111100
χ3166-6-3-3322000000-20000-1-10002i−2i10000−i−iii0066-6-3-3322000000-20000-1-10002i−2i10000−i−iii00
χ3266-6-3-3322000000-20000-1-1000−2i2i10000ii−i−i0066-6-3-3322000000-20000-1-1000−2i2i10000ii−i−i00
χ3366-6-3-33-2-2000000200001100000-10000−i3i3i3−i30066-6-3-33-2-2000000200001100000-10000−i3i3i3−i300
χ3466-6-3-33-2-2000000200001100000-10000i3−i3−i3i30066-6-3-33-2-2000000200001100000-10000i3−i3−i3i300
χ358-808-8000-4240-20000000000000000000000008-808-8000-4240-2000000000000000000000000
χ3612-120-6604i−4i00000000000−2i2i000000000000000012-120-6604i−4i00000000000−2i2i0000000000000000
χ3712-120-660−4i4i000000000002i−2i000000000000000012-120-660−4i4i000000000002i−2i0000000000000000
χ381111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ391111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111
χ40111111111111111-1-1-1-111111-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-111111111-1-1
χ41111111111111111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-11111-1-1-1-111
χ4211-111-1-1-1111-11-11ii−i−i-1-1-11-1i−i1ii−i−iii−i−i1-1-1-11-1-1111-1-1-11-11-1−i−iii111-11−ii-1−i−iii−i−iii-11
χ4311-111-1-1-1111-11-11ii−i−i-1-1-1-11−ii1ii−i−i−i−iii-11-1-11-1-1111-1-1-11-11-1−i−iii1111-1i−i-1−i−iiiii−i−i1-1
χ4411-111-1-1-1111-11-11−i−iii-1-1-11-1−ii1−i−iii−i−iii1-1-1-11-1-1111-1-1-11-11-1ii−i−i111-11i−i-1ii−i−iii−i−i-11
χ4511-111-1-1-1111-11-11−i−iii-1-1-1-11i−i1−i−iiiii−i−i-11-1-11-1-1111-1-1-11-11-1ii−i−i1111-1−ii-1ii−i−i−i−iii1-1
χ46222222-2-2222222-20000-2-220000-20000000000-2-2-2-2-2-222-2-2-2-2-2-22000022-2000020000000000
χ4722-222-222222-22-2-2000022-20000-20000000000-2-22-2-22-2-2-2-2-22-2220000-2-22000020000000000
χ482-202-202i−2i22-20-2001+i−1−i1−i−1+i2i−2i0000001+i−1−i1−i−1+i000000-220-220−2i2i-2-220200−1−i1+i−1+i1−i−2i2i000000−1−i1+i−1+i1−i000000
χ492-202-202i−2i22-20-200−1−i1+i−1+i1−i2i−2i000000−1−i1+i−1+i1−i000000-220-220−2i2i-2-2202001+i−1−i1−i−1+i−2i2i0000001+i−1−i1−i−1+i000000
χ502-202-20−2i2i22-20-2001−i−1+i1+i−1−i−2i2i0000001−i−1+i1+i−1−i000000-220-2202i−2i-2-220200−1+i1−i−1−i1+i2i−2i000000−1+i1−i−1−i1+i000000
χ512-202-20−2i2i22-20-200−1+i1−i−1−i1+i−2i2i000000−1+i1−i−1−i1+i000000-220-2202i−2i-2-2202001−i−1+i1+i−1−i2i−2i0000001−i−1+i1+i−1−i000000
χ52444444001-211-210222200-200000-1-1-1-1000000-4-4-4-4-4-400-12-1-12-10-2-2-2-2002000001111000000
χ53444444001-211-210-2-2-2-200-2000001111000000-4-4-4-4-4-400-12-1-12-10222200200000-1-1-1-1000000
χ5444444400-21-2-21-2000000012200000000000-1-1-4-4-4-4-4-4002-122-120000000-1-2-20000000000011
χ5544444400-21-2-21-200000001-2-20000000000011-4-4-4-4-4-4002-122-120000000-12200000000000-1-1
χ5644-444-4001-21-1-2-102i2i−2i−2i00200000−i−iii000000-4-44-4-4400-12-11210−2i−2i2i2i00-200000ii−i−i000000
χ5744-444-4001-21-1-2-10−2i−2i2i2i00200000ii−i−i000000-4-44-4-4400-12-112102i2i−2i−2i00-200000−i−iii000000
χ5844-444-400-21-22120000000-12-200000000000-11-4-44-4-44002-12-2-1-200000001-22000000000001-1
χ5944-444-400-21-22120000000-1-22000000000001-1-4-44-4-44002-12-2-1-2000000012-200000000000-11
χ604-404-40001-2-132-302-22-200000000-11-11000000-440-44000-121-3-230-22-22000000001-11-1000000
χ614-404-40001-2-132-30-22-22000000001-11-1000000-440-44000-121-3-2302-22-200000000-11-11000000
χ624-404-40001-2-1-32302i−2i−2i2i00000000−iii−i000000-440-44000-1213-2-30−2i2i2i−2i00000000i−i−ii000000
χ634-404-40001-2-1-3230−2i2i2i−2i00000000i−i−ii000000-440-44000-1213-2-302i−2i−2i2i00000000−iii−i000000
χ64666-3-3-32200000020000-1-100000-100003−33−300-6-6-6333-2-2000000-20000110000010000−33−3300
χ65666-3-3-32200000020000-1-100000-10000−33−3300-6-6-6333-2-2000000-200001100000100003−33−300
χ66666-3-3-3-2-2000000-20000110002210000-1-1-1-100-6-6-63332200000020000-1-1000-2-2-10000111100
χ67666-3-3-3-2-2000000-2000011000-2-210000111100-6-6-63332200000020000-1-100022-10000-1-1-1-100
χ6866-6-3-3322000000-20000-1-10002i−2i10000−i−iii00-6-6633-3-2-20000002000011000−2i2i-10000ii−i−i00
χ6966-6-3-3322000000-20000-1-1000−2i2i10000ii−i−i00-6-6633-3-2-200000020000110002i−2i-10000−i−iii00
χ7066-6-3-33-2-2000000200001100000-10000−i3i3i3−i300-6-6633-322000000-20000-1-10000010000i3−i3−i3i300
χ7166-6-3-33-2-2000000200001100000-10000i3−i3−i3i300-6-6633-322000000-20000-1-10000010000−i3i3i3−i300
χ728-808-8000-4240-2000000000000000000000000-880-880004-2-402000000000000000000000000
χ7312-120-6604i−4i00000000000−2i2i0000000000000000-121206-60−4i4i000000000002i−2i0000000000000000
χ7412-120-660−4i4i000000000002i−2i0000000000000000-121206-604i−4i00000000000−2i2i0000000000000000

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