Finite Group Databasebeta

← Group #72252361

Character table — Group #72252361

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1122222224444444444444444888888888888888888161616161616161616161616161616161616161616162424242424242424363636363636484848484848484848484848484848484848484872144144
order122223366222234466666666666666666666666121212124466121212121212121212121212121212121212224444442222224444661212121212121212121212121212444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-11-111-1-1-1-1-1-1-1-111-1-11-11-111-1-11111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111-11-11-1-111-1-1-1-1-1-1-1-111-11-11-1-111-1-1-1-11111-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ51111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1
χ61111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-1-1-1-1-1111-11-111-1-1-1-1-1-11111-111
χ71111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-111-1-1-11-11-1-1111111-1-1-1-1-111
χ81111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111-1-1
χ9111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111i−i-1-111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-11111-1-1i−ii−i1111-1-1-1-1ii−i−iii−i−i-1i−i
χ10111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111i−i-1-111iiiiiiii−i−i−i−i−i−i−i−i1-11-1-1-111-1-1-1-111i−i−ii1-11-1-1-111ii−i−i−i−iii1−ii
χ11111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111i−i-1-111iiiiiiii−i−i−i−i−i−i−i−i-11-1111-1-1-1-1-1-111−iii−i-11-1111-1-1−i−iiiii−i−i1−ii
χ12111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111i−i-1-111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111111111-1-1−ii−ii-1-1-1-11111−i−iii−i−iii-1i−i
χ13111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111−ii-1-111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-11111-1-1−ii−ii1111-1-1-1-1−i−iii−i−iii-1−ii
χ14111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111−ii-1-111−i−i−i−i−i−i−i−iiiiiiiii1-11-1-1-111-1-1-1-111−iii−i1-11-1-1-111−i−iiiii−i−i1i−i
χ15111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111−ii-1-111−i−i−i−i−i−i−i−iiiiiiiii-11-1111-1-1-1-1-1-111i−i−ii-11-1111-1-1ii−i−i−i−iii1i−i
χ16111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111−ii-1-111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111111111-1-1i−ii−i-1-1-1-11111ii−i−iii−i−i-1−ii
χ172222222222-2-222-2-222222222222-2-222222222-2-2-2-2-2-200-2-2-2-200000000000000000000000022-2-22200000000000000000000-200
χ182222222222-2-222-2-222222222222-2-222222222-2-2-2-2-2-200-2-2-2-2000000000000000000000000-2-222-2-200000000000000000000200
χ19222222222-222-22-2-2222222222-2-22222-2-2-2-2-2-222-2-2-2-20022-2-200000000000000000000000022-2-2-2-200000000000000000000200
χ20222222222-222-22-2-2222222222-2-22222-2-2-2-2-2-222-2-2-2-20022-2-2000000000000000000000000-2-2222200000000000000000000-200
χ21222222-12-12222-12222-1-1-1-1-12-12-12-1-1-1-1-12-1-1-12-122-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10202002200000000220-10-100-1-10000-1-1-1-1000
χ22222222-12-12222-12222-1-1-1-1-12-12-12-1-1-1-1-12-1-1-12-122-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10-20-200-2-200000000-2-20101001100001111000
χ23222222-12-12222-12222-1-1-1-1-12-12-12-1-1-1-1-12-1-1-12-122-1-1-2-2-1-1-1-1-2-2111111-2-21111110202002200000000-2-20-10-100-1-100001111000
χ24222222-12-12222-12222-1-1-1-1-12-12-12-1-1-1-1-12-1-1-12-122-1-1-2-2-1-1-1-1-2-2111111-2-21111110-20-200-2-20000000022010100110000-1-1-1-1000
χ25222222-12-1-2-2-2-2-12222-1-1-1-1-12-1-21-21-1-111-2111-2122-1-12i−2i11-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii020200-2-2000000002i−2i0-10-100110000−i−iii000
χ26222222-12-1-2-2-2-2-12222-1-1-1-1-12-1-21-21-1-111-2111-2122-1-12i−2i11-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii0-20-2002200000000−2i2i010100-1-10000ii−i−i000
χ27222222-12-1-2-2-2-2-12222-1-1-1-1-12-1-21-21-1-111-2111-2122-1-1−2i2i11-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i020200-2-200000000−2i2i0-10-100110000ii−i−i000
χ28222222-12-1-2-2-2-2-12222-1-1-1-1-12-1-21-21-1-111-2111-2122-1-1−2i2i11-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i0-20-20022000000002i−2i010100-1-10000−i−iii000
χ2922222-12-122222-122-1-122-1-1-1-12-12-12-1-1-1-1-12-1-1-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1202022000000002200-10-10-1-100-1-1-1-10000000
χ3022222-12-122222-122-1-122-1-1-1-12-12-12-1-1-1-1-12-1-1-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-20-20-2-200000000-2-2001010110011110000000
χ3122222-12-122222-122-1-122-1-1-1-12-12-12-1-1-1-1-12-1-1-12-1-122-2-2-1-1-1-111-2-2111111-2-2111120202200000000-2-200-10-10-1-10011110000000
χ3222222-12-122222-122-1-122-1-1-1-12-12-12-1-1-1-1-12-1-1-12-1-122-2-2-1-1-1-111-2-2111111-2-21111-20-20-2-200000000220010101100-1-1-1-10000000
χ3322222-12-12-2-2-2-2-122-1-122-1-1-1-121-21-2-1-1111-2111-2-1-1222i−2i11-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii2020-2-2000000002i−2i00-10-101100−i−iii0000000
χ3422222-12-12-2-2-2-2-122-1-122-1-1-1-121-21-2-1-1111-2111-2-1-1222i−2i11-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii-20-202200000000−2i2i001010-1-100ii−i−i0000000
χ3522222-12-12-2-2-2-2-122-1-122-1-1-1-121-21-2-1-1111-2111-2-1-122−2i2i11-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i2020-2-200000000−2i2i00-10-101100ii−i−i0000000
χ3622222-12-12-2-2-2-2-122-1-122-1-1-1-121-21-2-1-1111-2111-2-1-122−2i2i11-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i-20-2022000000002i−2i001010-1-100−i−iii0000000
χ3722-2-22222222-2-222-2-2-2-2-2-2-2222-2-22-22-2-2-22222-222-22-2002-22-20000000000000000020-2002-20000000000020-2002-200000000000
χ3822-2-22222222-2-222-2-2-2-2-2-2-2222-2-22-22-2-2-22222-222-22-2002-22-200000000000000000-20200-2200000000000-20200-2200000000000
χ3922-2-2222222-22-22-22-2-2-2-2-2-2222-2-2-222-2-2-222222-2-22-2200-22-22000000000000000020-202-200000000000020-202-20000000000000
χ4022-2-2222222-22-22-22-2-2-2-2-2-2222-2-2-222-2-2-222222-2-22-2200-22-220000000000000000-2020-22000000000000-2020-220000000000000
χ4122-2-222222-22-222-22-2-2-2-2-2-2222222-22-222-2-2-2-2-22-22-22002-2-22000000000000000020-20-2200000000000020-20-220000000000000
χ4222-2-222222-22-222-22-2-2-2-2-2-2222222-22-222-2-2-2-2-22-22-22002-2-220000000000000000-20202-2000000000000-20202-20000000000000
χ4322-2-222222-2-22222-2-2-2-2-2-2-222222-222-222-2-2-2-22-22-22-200-222-20000000000000000020-200-220000000000020-200-2200000000000
χ4422-2-222222-2-22222-2-2-2-2-2-2-222222-222-222-2-2-2-22-22-22-200-222-200000000000000000-202002-200000000000-202002-200000000000
χ4522-2-222-12-122-2-2-12-2-2-21111-12-1-2121-11112-1-1-1-2-12-2-1100-11-1100−i3i3−i3−i3i3i300−i3i3−i3−i3i3i3020-2002-200000000000-10100-110000−i3i3−i3i3000
χ4622-2-222-12-122-2-2-12-2-2-21111-12-1-2121-11112-1-1-1-2-12-2-1100-11-1100−i3i3−i3−i3i3i300−i3i3−i3−i3i3i30-20200-220000000000010-1001-10000i3−i3i3−i3000
χ4722-2-222-12-122-2-2-12-2-2-21111-12-1-2121-11112-1-1-1-2-12-2-1100-11-1100i3−i3i3i3−i3−i300i3−i3i3i3−i3−i3020-2002-200000000000-10100-110000i3−i3i3−i3000
χ4822-2-222-12-122-2-2-12-2-2-21111-12-1-2121-11112-1-1-1-2-12-2-1100-11-1100i3−i3i3i3−i3−i300i3−i3i3i3−i3−i30-20200-220000000000010-1001-10000−i3i3−i3i3000
χ4922-2-222-12-1-2-222-12-2-2-21111-12-12-1-2-1-11-1-1-2111212-2-11001-1-11003−333−3−300−33−3−333020-200-2200000000000-101001-100003−3−33000
χ5022-2-222-12-1-2-222-12-2-2-21111-12-12-1-2-1-11-1-1-2111212-2-11001-1-11003−333−3−300−33−3−3330-202002-20000000000010-100-110000−333−3000
χ5122-2-222-12-1-2-222-12-2-2-21111-12-12-1-2-1-11-1-1-2111212-2-11001-1-1100−33−3−333003−333−3−3020-200-2200000000000-101001-10000−333−3000
χ5222-2-222-12-1-2-222-12-2-2-21111-12-12-1-2-1-11-1-1-2111212-2-11001-1-1100−33−3−333003−333−3−30-202002-20000000000010-100-1100003−3−33000
χ5322-2-22-12-122-22-2-1-2211-2-211-1-121-212-1111-12-1-1-1-21-1-22001-11-1−i3i300−i3i3−i3i3−i3i300−i3i3−i3i320-202-2000000000000-1010-1100−i3i3−i3i30000000
χ5422-2-22-12-122-22-2-1-2211-2-211-1-121-212-1111-12-1-1-1-21-1-22001-11-1−i3i300−i3i3−i3i3−i3i300−i3i3−i3i3-2020-2200000000000010-101-100i3−i3i3−i30000000
χ5522-2-22-12-122-22-2-1-2211-2-211-1-121-212-1111-12-1-1-1-21-1-22001-11-1i3−i300i3−i3i3−i3i3−i300i3−i3i3−i320-202-2000000000000-1010-1100i3−i3i3−i30000000
χ5622-2-22-12-122-22-2-1-2211-2-211-1-121-212-1111-12-1-1-1-21-1-22001-11-1i3−i300i3−i3i3−i3i3−i300i3−i3i3−i3-2020-2200000000000010-101-100−i3i3−i3i30000000
χ5722-2-22-12-12-22-22-1-2211-2-211-1-12-12-1-2-11-1-11-211121-1-2200-111-13−3003−33−3−3300−33−3320-20-22000000000000-10101-1003−3−330000000
χ5822-2-22-12-12-22-22-1-2211-2-211-1-12-12-1-2-11-1-11-211121-1-2200-111-13−3003−33−3−3300−33−33-20202-200000000000010-10-1100−333−30000000
χ5922-2-22-12-12-22-22-1-2211-2-211-1-12-12-1-2-11-1-11-211121-1-2200-111-1−3300−33−333−3003−33−320-20-22000000000000-10101-100−333−30000000
χ6022-2-22-12-12-22-22-1-2211-2-211-1-12-12-1-2-11-1-11-211121-1-2200-111-1−3300−33−333−3003−33−3-20202-200000000000010-10-11003−3−330000000
χ61444444-24-24-4-44-2-4-444-2-2-2-2-24-24-2-42-2-2-2-24-2-2-2-42-4-42200222200000000000000000000000000000000000000000000000000000
χ62444444-24-2-444-4-2-4-444-2-2-2-2-24-2-424-2-2-222-42224-2-4-42200-2-22200000000000000000000000000000000000000000000000000000
χ6344444-24-244-4-44-2-4-4-2-244-2-2-2-24-242-4-2-2-2-2-24-2-22-422-4-400222200000000000000000000000000000000000000000000000000000
χ6444444-24-24-444-4-2-4-4-2-244-2-2-2-242-4-24-2-2222-422-2422-4-400-2-22200000000000000000000000000000000000000000000000000000
χ6544444-2-2-2-24444144-2-2-2-2111-2-2-2-2-2-21111-2-211-2-2-2-2-2-2441111-2-2-2-21111-2-2-2-211110000000000000000000000000000000000000
χ6644444-2-2-2-24444144-2-2-2-2111-2-2-2-2-2-21111-2-211-2-2-2-2-2-2-4-411112222-1-1-1-12222-1-1-1-10000000000000000000000000000000000000
χ6744444-2-2-2-24-4-441-4-4-2-2-2-2111-2-2-2-2221111-2-21122222200-1-1-1-100003-3-3300003-3-330000000000000000000000000000000000000
χ6844444-2-2-2-24-4-441-4-4-2-2-2-2111-2-2-2-2221111-2-21122222200-1-1-1-10000-333-30000-333-30000000000000000000000000000000000000
χ6944444-2-2-2-2-444-41-4-4-2-2-2-2111-2-222-2-211-1-122-1-1-2-222220011-1-100003i−3i−3i3i0000−3i3i3i−3i0000000000000000000000000000000000000
χ7044444-2-2-2-2-444-41-4-4-2-2-2-2111-2-222-2-211-1-122-1-1-2-222220011-1-10000−3i3i3i−3i00003i−3i−3i3i0000000000000000000000000000000000000
χ7144444-2-2-2-2-4-4-4-4144-2-2-2-2111-2-2222211-1-122-1-122-2-2-2-24i−4i-1-111−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000000000000000000000000000000000000
χ7244444-2-2-2-2-4-4-4-4144-2-2-2-2111-2-2222211-1-122-1-122-2-2-2-2−4i4i-1-1112i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii0000000000000000000000000000000000000
χ73444-4-4444400004004-44-4444-4-40000-4-40000000000000000000000000000000000000000004-4000000000000000000000000000
χ74444-4-4444400004004-44-4444-4-40000-4-4000000000000000000000000000000000000000000-44000000000000000000000000000
χ7544-44-444440000400-44-44-4-44-4-40000-44000000000000000000000000000000000000000000004-40000000000000000000000000
χ7644-44-444440000400-44-44-4-44-4-40000-4400000000000000000000000000000000000000000000-440000000000000000000000000
χ7744-4-444-24-24-44-4-2-44-4-42222-24-2-42-4-2-22224-2-2-242-442-2002-22-200000000000000000000000000000000000000000000000000000
χ7844-4-444-24-2-44-44-2-44-4-42222-24-24-242-22-2-2-4222-4-2-442-200-222-200000000000000000000000000000000000000000000000000000
χ7944-4-44-24-2444-4-4-24-422-4-422-2-242-4-2-4-2222-24-2-224-224-400-22-2200000000000000000000000000000000000000000000000000000
χ8044-4-44-24-24-4-444-24-422-4-422-2-24-2424-22-2-22-422-2-4-224-4002-2-2200000000000000000000000000000000000000000000000000000
χ8144-4-44-2-2-2-244-4-414-42222-1-11-2-222-221-1-1-1-2-2112-2-22-22001-11-100−2i32i3i3i3−i3−i300−2i32i3i3i3−i3−i30000000000000000000000000000000000000
χ8244-4-44-2-2-2-244-4-414-42222-1-11-2-222-221-1-1-1-2-2112-2-22-22001-11-1002i3−2i3−i3−i3i3i3002i3−2i3−i3−i3i3i30000000000000000000000000000000000000
χ8344-4-44-2-2-2-24-44-41-442222-1-11-2-2222-21-1-1-1-2-211-222-22-200-11-11−2i32i300i3−i3i3−i3−2i32i300i3−i3i3−i30000000000000000000000000000000000000
χ8444-4-44-2-2-2-24-44-41-442222-1-11-2-2222-21-1-1-1-2-211-222-22-200-11-112i3−2i300−i3i3−i3i32i3−2i300−i3i3−i3i30000000000000000000000000000000000000
χ8544-4-44-2-2-2-2-44-441-442222-1-11-2-2-2-2-221-11122-1-12-22-22-2001-1-1123−2300−33−33−2323003−33−30000000000000000000000000000000000000
χ8644-4-44-2-2-2-2-44-441-442222-1-11-2-2-2-2-221-11122-1-12-22-22-2001-1-11−2323003−33−323−2300−33−330000000000000000000000000000000000000
χ8744-4-44-2-2-2-2-4-44414-42222-1-11-2-2-2-22-21-11122-1-1-22-22-2200-111-10023−23−3−33300−232333−3−30000000000000000000000000000000000000
χ8844-4-44-2-2-2-2-4-44414-42222-1-11-2-2-2-22-21-11122-1-1-22-22-2200-111-100−232333−3−30023−23−3−3330000000000000000000000000000000000000
χ89888-8-88-48-40000-4008-8-44-4-4-4-8400004400000000000000000000000000000000000000000000000000000000000000000000000
χ90888-8-8-48-480000-400-448-8-4-4-44-800004400000000000000000000000000000000000000000000000000000000000000000000000
χ91888-8-8-4-4-4-40000200-44-44222440000-2-26-6006-600000000000000000000000000000000000000000000000000000000000000000
χ92888-8-8-4-4-4-40000200-44-44222440000-2-2-6600-6600000000000000000000000000000000000000000000000000000000000000000
χ9388-88-88-48-40000-400-884-444-4-8400004-400000000000000000000000000000000000000000000000000000000000000000000000
χ9488-88-8-48-480000-4004-4-8844-44-800004-400000000000000000000000000000000000000000000000000000000000000000000000
χ9588-88-8-4-4-4-400002004-44-4-2-22440000-226-600-6600000000000000000000000000000000000000000000000000000000000000000
χ9688-88-8-4-4-4-400002004-44-4-2-22440000-22-66006-600000000000000000000000000000000000000000000000000000000000000000
χ978-800088-8-80000800000000-80000000000000000000000000000000000000000000000000000004-400000000000000000000000
χ988-800088-8-80000800000000-8000000000000000000000000000000000000000000000000000000-4400000000000000000000000
χ9916-1600016-8-1680000-80000000080000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10016-16000-8168-160000-80000000080000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10116-16000-8-8880000400000012-12-40000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10216-16000-8-88800004000000-1212-40000000000000000000000000000000000000000000000000000000000000000000000000000000

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