Finite Group Databasebeta

← Group #72341349

Character table — Group #72341349

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size11113333666666668824242424242424242424242424242424242432323232323232321111333366666666882424242424242424242424242424242424243232323232323232
order1222222222222222224444444444444444443666666622222222222222222244444444444444444466666666
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ31111111111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111111111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ511-1-111-1-11111-1-1-1-11-1i−ii−i1-1i−ii−iii−i−iii−i−i11-1-111-1-111-1-111-1-11111-1-1-1-11-1i−ii−i1-1i−ii−iii−i−iii−i−i11-1-111-1-1
χ611-1-111-1-11111-1-1-1-11-1−ii−ii1-1−ii−ii−i−iii−i−iii11-1-111-1-111-1-111-1-11111-1-1-1-11-1−ii−ii1-1−ii−ii−i−iii−i−iii11-1-111-1-1
χ711-1-111-1-11111-1-1-1-1-11i−i−ii-11i−i−iiii−i−i−i−iii11-1-1-1-11111-1-111-1-11111-1-1-1-1-11i−i−ii-11i−i−iiii−i−i−i−iii11-1-1-1-111
χ811-1-111-1-11111-1-1-1-1-11−iii−i-11−iii−i−i−iiiii−i−i11-1-1-1-11111-1-111-1-11111-1-1-1-1-11−iii−i-11−iii−i−i−iiiii−i−i11-1-1-1-111
χ9222222222222222222000022000000000000-1-1-1-1-1-1-1-1222222222222222222000022000000000000-1-1-1-1-1-1-1-1
χ102222222222222222-2-20000-2-2000000000000-1-1-1-111112222222222222222-2-20000-2-2000000000000-1-1-1-11111
χ1122-2-222-2-22222-2-2-2-22-200002-2000000000000-1-111-1-11122-2-222-2-22222-2-2-2-22-200002-2000000000000-1-111-1-111
χ1222-2-222-2-22222-2-2-2-2-220000-22000000000000-1-11111-1-122-2-222-2-22222-2-2-2-2-220000-22000000000000-1-11111-1-1
χ132-22-2-222-222-2-22-22-2000000000000000000002-22-200002-22-2-222-222-2-22-22-2000000000000000000002-22-20000
χ142-22-2-222-222-2-22-22-200000000000000000000-11-11−i3i3−i3i32-22-2-222-222-2-22-22-200000000000000000000-11-11−i3i3−i3i3
χ152-22-2-222-222-2-22-22-200000000000000000000-11-11i3−i3i3−i32-22-2-222-222-2-22-22-200000000000000000000-11-11i3−i3i3−i3
χ162-2-22-22-2222-2-2-22-22000000000000000000002-2-2200002-2-22-22-2222-2-2-22-22000000000000000000002-2-220000
χ172-2-22-22-2222-2-2-22-2200000000000000000000-111-1−i3i3i3−i32-2-22-22-2222-2-2-22-2200000000000000000000-111-1−i3i3i3−i3
χ182-2-22-22-2222-2-2-22-2200000000000000000000-111-1i3−i3−i3i32-2-22-22-2222-2-2-22-2200000000000000000000-111-1i3−i3−i3i3
χ1933333333-1-1-1-1-1-1-1-1331111-1-11111-1-1-1-1-1-1-1-10000000033333333-1-1-1-1-1-1-1-1331111-1-11111-1-1-1-1-1-1-1-100000000
χ2033333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1111111110000000033333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-11111111100000000
χ2133333333-1-1-1-1-1-1-1-1-3-311-1-11111-1-1-1-1-1-111110000000033333333-1-1-1-1-1-1-1-1-3-311-1-11111-1-1-1-1-1-1111100000000
χ2233333333-1-1-1-1-1-1-1-1-3-3-1-11111-1-1111111-1-1-1-10000000033333333-1-1-1-1-1-1-1-1-3-3-1-11111-1-1111111-1-1-1-100000000
χ2333-3-333-3-3-1-1-1-111113-3i−ii−i-11i−ii−i−i−iii−i−iii0000000033-3-333-3-3-1-1-1-111113-3i−ii−i-11i−ii−i−i−iii−i−iii00000000
χ2433-3-333-3-3-1-1-1-111113-3−ii−ii-11−ii−iiii−i−iii−i−i0000000033-3-333-3-3-1-1-1-111113-3−ii−ii-11−ii−iiii−i−iii−i−i00000000
χ2533-3-333-3-3-1-1-1-11111-33i−i−ii1-1i−i−ii−i−iiiii−i−i0000000033-3-333-3-3-1-1-1-11111-33i−i−ii1-1i−i−ii−i−iiiii−i−i00000000
χ2633-3-333-3-3-1-1-1-11111-33−iii−i1-1−iii−iii−i−i−i−iii0000000033-3-333-3-3-1-1-1-11111-33−iii−i1-1−iii−iii−i−i−i−iii00000000
χ276666-2-2-2-22-22-22-2-220000220000-2-200000000000000006666-2-2-2-22-22-22-2-220000220000-2-20000000000000000
χ286666-2-2-2-22-22-22-2-220000-2-200002200000000000000006666-2-2-2-22-22-22-2-220000-2-20000220000000000000000
χ296666-2-2-2-2-22-22-222-200220000-2-20000000000000000006666-2-2-2-2-22-22-222-200220000-2-2000000000000000000
χ306666-2-2-2-2-22-22-222-200-2-20000220000000000000000006666-2-2-2-2-22-22-222-200-2-2000022000000000000000000
χ3166-6-6-2-2222-22-2-222-200002i−2i0000−2i2i000000000000000066-6-6-2-2222-22-2-222-200002i−2i0000−2i2i0000000000000000
χ3266-6-6-2-2222-22-2-222-20000−2i2i00002i−2i000000000000000066-6-6-2-2222-22-2-222-20000−2i2i00002i−2i0000000000000000
χ3366-6-6-2-222-22-222-2-22002i−2i0000−2i2i00000000000000000066-6-6-2-222-22-222-2-22002i−2i0000−2i2i000000000000000000
χ3466-6-6-2-222-22-222-2-2200−2i2i00002i−2i00000000000000000066-6-6-2-222-22-222-2-2200−2i2i00002i−2i000000000000000000
χ356-66-62-2-222-2-2222-2-200000000000000002i−2i2i−2i000000006-66-62-2-222-2-2222-2-200000000000000002i−2i2i−2i00000000
χ366-66-62-2-222-2-2222-2-20000000000000000−2i2i−2i2i000000006-66-62-2-222-2-2222-2-20000000000000000−2i2i−2i2i00000000
χ376-66-62-2-22-222-2-2-2220000000000002-22-20000000000006-66-62-2-22-222-2-2-2220000000000002-22-2000000000000
χ386-66-62-2-22-222-2-2-222000000000000-22-220000000000006-66-62-2-22-222-2-2-222000000000000-22-22000000000000
χ396-66-6-666-6-2-222-22-2200000000000000000000000000006-66-6-666-6-2-222-22-220000000000000000000000000000
χ406-6-662-22-22-2-22-2-22200000000000000002-2-22000000006-6-662-22-22-2-22-2-22200000000000000002-2-2200000000
χ416-6-662-22-22-2-22-2-2220000000000000000-222-2000000006-6-662-22-22-2-22-2-2220000000000000000-222-200000000
χ426-6-662-22-2-222-222-2-20000000000002i−2i−2i2i0000000000006-6-662-22-2-222-222-2-20000000000002i−2i−2i2i000000000000
χ436-6-662-22-2-222-222-2-2000000000000−2i2i2i−2i0000000000006-6-662-22-2-222-222-2-2000000000000−2i2i2i−2i000000000000
χ446-6-66-66-66-2-2222-22-200000000000000000000000000006-6-66-66-66-2-2222-22-20000000000000000000000000000
χ4511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ46111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1
χ471111111111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-11111
χ481111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ4911-1-111-1-11111-1-1-1-11-1i−ii−i1-1i−ii−iii−i−iii−i−i11-1-111-1-1-1-111-1-111-1-1-1-11111-11−ii−ii-11−ii−ii−i−iii−i−iii-1-111-1-111
χ5011-1-111-1-11111-1-1-1-11-1−ii−ii1-1−ii−ii−i−iii−i−iii11-1-111-1-1-1-111-1-111-1-1-1-11111-11i−ii−i-11i−ii−iii−i−iii−i−i-1-111-1-111
χ5111-1-111-1-11111-1-1-1-1-11i−i−ii-11i−i−iiii−i−i−i−iii11-1-1-1-111-1-111-1-111-1-1-1-111111-1−iii−i1-1−iii−i−i−iiiii−i−i-1-11111-1-1
χ5211-1-111-1-11111-1-1-1-1-11−iii−i-11−iii−i−i−iiiii−i−i11-1-1-1-111-1-111-1-111-1-1-1-111111-1i−i−ii1-1i−i−iiii−i−i−i−iii-1-11111-1-1
χ53222222222222222222000022000000000000-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000-2-200000000000011111111
χ542222222222222222-2-20000-2-2000000000000-1-1-1-11111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2220000220000000000001111-1-1-1-1
χ5522-2-222-2-22222-2-2-2-22-200002-2000000000000-1-111-1-111-2-222-2-222-2-2-2-22222-220000-2200000000000011-1-111-1-1
χ5622-2-222-2-22222-2-2-2-2-220000-22000000000000-1-11111-1-1-2-222-2-222-2-2-2-222222-200002-200000000000011-1-1-1-111
χ572-22-2-222-222-2-22-22-2000000000000000000002-22-20000-22-222-2-22-2-222-22-2200000000000000000000-22-220000
χ582-22-2-222-222-2-22-22-200000000000000000000-11-11−i3i3−i3i3-22-222-2-22-2-222-22-22000000000000000000001-11-1i3−i3i3−i3
χ592-22-2-222-222-2-22-22-200000000000000000000-11-11i3−i3i3−i3-22-222-2-22-2-222-22-22000000000000000000001-11-1−i3i3−i3i3
χ602-2-22-22-2222-2-2-22-22000000000000000000002-2-220000-222-22-22-2-2-2222-22-200000000000000000000-222-20000
χ612-2-22-22-2222-2-2-22-2200000000000000000000-111-1−i3i3i3−i3-222-22-22-2-2-2222-22-2000000000000000000001-1-11i3−i3−i3i3
χ622-2-22-22-2222-2-2-22-2200000000000000000000-111-1i3−i3−i3i3-222-22-22-2-2-2222-22-2000000000000000000001-1-11−i3i3i3−i3
χ6333333333-1-1-1-1-1-1-1-1331111-1-11111-1-1-1-1-1-1-1-100000000-3-3-3-3-3-3-3-311111111-3-3-1-1-1-111-1-1-1-11111111100000000
χ6433333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-11111111100000000-3-3-3-3-3-3-3-311111111-3-31111111111-1-1-1-1-1-1-1-100000000
χ6533333333-1-1-1-1-1-1-1-1-3-311-1-11111-1-1-1-1-1-1111100000000-3-3-3-3-3-3-3-31111111133-1-111-1-1-1-1111111-1-1-1-100000000
χ6633333333-1-1-1-1-1-1-1-1-3-3-1-11111-1-1111111-1-1-1-100000000-3-3-3-3-3-3-3-3111111113311-1-1-1-111-1-1-1-1-1-1111100000000
χ6733-3-333-3-3-1-1-1-111113-3i−ii−i-11i−ii−i−i−iii−i−iii00000000-3-333-3-3331111-1-1-1-1-33−ii−ii1-1−ii−iiii−i−iii−i−i00000000
χ6833-3-333-3-3-1-1-1-111113-3−ii−ii-11−ii−iiii−i−iii−i−i00000000-3-333-3-3331111-1-1-1-1-33i−ii−i1-1i−ii−i−i−iii−i−iii00000000
χ6933-3-333-3-3-1-1-1-11111-33i−i−ii1-1i−i−ii−i−iiiii−i−i00000000-3-333-3-3331111-1-1-1-13-3−iii−i-11−iii−iii−i−i−i−iii00000000
χ7033-3-333-3-3-1-1-1-11111-33−iii−i1-1−iii−iii−i−i−i−iii00000000-3-333-3-3331111-1-1-1-13-3i−i−ii-11i−i−ii−i−iiiii−i−i00000000
χ716666-2-2-2-22-22-22-2-220000220000-2-20000000000000000-6-6-6-62222-22-22-222-20000-2-20000220000000000000000
χ726666-2-2-2-22-22-22-2-220000-2-20000220000000000000000-6-6-6-62222-22-22-222-20000220000-2-20000000000000000
χ736666-2-2-2-2-22-22-222-200220000-2-2000000000000000000-6-6-6-622222-22-22-2-2200-2-2000022000000000000000000
χ746666-2-2-2-2-22-22-222-200-2-2000022000000000000000000-6-6-6-622222-22-22-2-2200220000-2-2000000000000000000
χ7566-6-6-2-2222-22-2-222-200002i−2i0000−2i2i0000000000000000-6-66622-2-2-22-222-2-220000−2i2i00002i−2i0000000000000000
χ7666-6-6-2-2222-22-2-222-20000−2i2i00002i−2i0000000000000000-6-66622-2-2-22-222-2-2200002i−2i0000−2i2i0000000000000000
χ7766-6-6-2-222-22-222-2-22002i−2i0000−2i2i000000000000000000-6-66622-2-22-22-2-222-200−2i2i00002i−2i000000000000000000
χ7866-6-6-2-222-22-222-2-2200−2i2i00002i−2i000000000000000000-6-66622-2-22-22-2-222-2002i−2i0000−2i2i000000000000000000
χ796-66-62-2-222-2-2222-2-200000000000000002i−2i2i−2i00000000-66-66-222-2-222-2-2-2220000000000000000−2i2i−2i2i00000000
χ806-66-62-2-222-2-2222-2-20000000000000000−2i2i−2i2i00000000-66-66-222-2-222-2-2-22200000000000000002i−2i2i−2i00000000
χ816-66-62-2-22-222-2-2-2220000000000002-22-2000000000000-66-66-222-22-2-2222-2-2000000000000-22-22000000000000
χ826-66-62-2-22-222-2-2-222000000000000-22-22000000000000-66-66-222-22-2-2222-2-20000000000002-22-2000000000000
χ836-66-6-666-6-2-222-22-220000000000000000000000000000-66-666-6-6622-2-22-22-20000000000000000000000000000
χ846-6-662-22-22-2-22-2-22200000000000000002-2-2200000000-666-6-22-22-222-222-2-20000000000000000-222-200000000
χ856-6-662-22-22-2-22-2-2220000000000000000-222-200000000-666-6-22-22-222-222-2-200000000000000002-2-2200000000
χ866-6-662-22-2-222-222-2-20000000000002i−2i−2i2i000000000000-666-6-22-222-2-22-2-222000000000000−2i2i2i−2i000000000000
χ876-6-662-22-2-222-222-2-2000000000000−2i2i2i−2i000000000000-666-6-22-222-2-22-2-2220000000000002i−2i−2i2i000000000000
χ886-6-66-66-66-2-2222-22-20000000000000000000000000000-666-66-66-622-2-2-22-220000000000000000000000000000

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