Finite Group Databasebeta

← Group #72252334

Character table — Group #72252334

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1122222224444444444444444888888888888888888161616161616161616161616161616161616161616162424242424242424363636363636484848484848484848484848484848484848484872144144
order122223366222234466666666666666666666666121212124466121212121212121212121212121212121212224444442222446688881212121212122424242424242424244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-11-111-1-1-1-1-1-1-1-11-111-1-11-111-1-11111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111-11-11-1-111-1-1-1-1-1-1-11-1-111-11-1-111-1-1-1-11111-1-1-1
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
χ51111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1
χ61111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-1-1-11-1-1-1111-111-1-1-1-1-1-11111-111
χ71111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1111-1-1-11-1-1111111-1-1-1-1-111
χ81111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1111111111-1-1
χ911111111111-1-11-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-111-1-11111i−ii−i11-1-1-1-1ii−i−iii−i−i-1i−i
χ1011111111111-1-11-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1-1-111-1-111-1-11-1i−i−ii1-1-1-111ii−i−i−i−iii1−ii
χ1111111111111-1-11-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-1111-1-1-1-111-1-1-11−iii−i-1111-1-1−i−iiiii−i−i1−ii
χ1211111111111-1-11-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1111111-1-111-1-1−ii−ii-1-11111−i−iii−i−iii-1i−i
χ1311111111111-1-11-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1−ii11-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-111-1-11111−ii−ii11-1-1-1-1−i−iii−i−iii-1−ii
χ1411111111111-1-11-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1−ii11-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1-1-111-1-111-1-11-1−iii−i1-1-1-111−i−iiiii−i−i1i−i
χ1511111111111-1-11-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1−ii11-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-1111-1-1-1-111-1-1-11i−i−ii-1111-1-1ii−i−i−i−iii1i−i
χ1611111111111-1-11-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1−ii11-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1111111-1-111-1-1i−ii−i-1-11111ii−i−iii−i−i-1−ii
χ17222222222-2-2222-2-2222222222-2-2-2-22222222222-2-2-2-200-2-2-2-20000000000000000000000002222-2-200000000000000000000-200
χ18222222222-2-2222-2-2222222222-2-2-2-22222222222-2-2-2-200-2-2-2-2000000000000000000000000-2-2-2-22200000000000000000000200
χ19222222222-2-2-2-2222222222222-2-2-2-2-2-222-2-2-2-2-2-2222200-2-22200000000000000000000000022-2-2-2-200000000000000000000200
χ20222222222-2-2-2-2222222222222-2-2-2-2-2-222-2-2-2-2-2-2222200-2-222000000000000000000000000-2-2222200000000000000000000-200
χ21222222-12-12222-12222-1-1-1-1-12-122-1-12-1-1-1-1-12-1-1-12-12-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1020200220000000-100220-100-1-10000-1-1-1-1000
χ22222222-12-12222-12222-1-1-1-1-12-122-1-12-1-1-1-1-12-1-1-12-12-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10-20-200-2-20000000100-2-201001100001111000
χ23222222-12-12222-12222-1-1-1-1-12-122-1-12-1-1-1-1-12-1-1-12-12-1-2-2-1-1-1-1-2-2111111-2-2111111020200220000000-100-2-20-100-1-100001111000
χ24222222-12-12222-12222-1-1-1-1-12-122-1-12-1-1-1-1-12-1-1-12-12-1-2-2-1-1-1-1-2-2111111-2-21111110-20-200-2-20000000100220100110000-1-1-1-1000
χ25222222-12-122-2-2-1-2-222-1-1-1-1-12-122-1-1-21-1-111-2111-21-212i−2i-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii020200-2-20000000-1002i−2i0-100110000−i−iii000
χ26222222-12-122-2-2-1-2-222-1-1-1-1-12-122-1-1-21-1-111-2111-21-212i−2i-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii0-20-200220000000100−2i2i0100-1-10000ii−i−i000
χ27222222-12-122-2-2-1-2-222-1-1-1-1-12-122-1-1-21-1-111-2111-21-21−2i2i-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i020200-2-20000000-100−2i2i0-100110000ii−i−i000
χ28222222-12-122-2-2-1-2-222-1-1-1-1-12-122-1-1-21-1-111-2111-21-21−2i2i-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i0-20-2002200000001002i−2i0100-1-10000−i−iii000
χ2922222-12-122222-122-1-122-1-1-1-12-1-122-12-1-1-1-1-12-1-1-12-1222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-120202200000000-102200-10-1-100-1-1-1-10000000
χ3022222-12-122222-122-1-122-1-1-1-12-1-122-12-1-1-1-1-12-1-1-12-1222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-20-20-2-20000000010-2-20010110011110000000
χ3122222-12-122222-122-1-122-1-1-1-12-1-122-12-1-1-1-1-12-1-1-12-12-2-2-1-1-1-111-2-2111111-2-2111120202200000000-10-2-200-10-1-10011110000000
χ3222222-12-122222-122-1-122-1-1-1-12-1-122-12-1-1-1-1-12-1-1-12-12-2-2-1-1-1-111-2-2111111-2-21111-20-20-2-200000000102200101100-1-1-1-10000000
χ3322222-12-1222-2-2-1-2-2-1-122-1-1-1-12-1-1221-2-1-1111-2111-21-22i−2i-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii2020-2-200000000-102i−2i00-101100−i−iii0000000
χ3422222-12-1222-2-2-1-2-2-1-122-1-1-1-12-1-1221-2-1-1111-2111-21-22i−2i-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii-20-20220000000010−2i2i0010-1-100ii−i−i0000000
χ3522222-12-1222-2-2-1-2-2-1-122-1-1-1-12-1-1221-2-1-1111-2111-21-2−2i2i-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i2020-2-200000000-10−2i2i00-101100ii−i−i0000000
χ3622222-12-1222-2-2-1-2-2-1-122-1-1-1-12-1-1221-2-1-1111-2111-21-2−2i2i-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i-20-202200000000102i−2i0010-1-100−i−iii0000000
χ3722-2-2222222-22-222-2-2-2-2-2-2-22222-22-2-2-22-2-2-222222-2-22002-22-20000000000000000020-2002-20000000200000-2002-200000000000
χ3822-2-2222222-22-222-2-2-2-2-2-2-22222-22-2-2-22-2-2-222222-2-22002-22-200000000000000000-20200-220000000-200000200-2200000000000
χ3922-2-2222222-2-222-22-2-2-2-2-2-22222-22-2222-222-2-2-2-2-222-2002-2-220000000000000000020-200-220000000200000-200-2200000000000
χ4022-2-2222222-2-222-22-2-2-2-2-2-22222-22-2222-222-2-2-2-2-222-2002-2-2200000000000000000-202002-20000000-2000002002-200000000000
χ4122-2-222222-222-22-22-2-2-2-2-2-2222-22-22-2-22-2-2-22222-222-200-22-22000000000000000020-202-200000000200000-202-20000000000000
χ4222-2-222222-222-22-22-2-2-2-2-2-2222-22-22-2-22-2-2-22222-222-200-22-220000000000000000-2020-2200000000-20000020-220000000000000
χ4322-2-222222-22-2222-2-2-2-2-2-2-2222-22-22222-222-2-2-2-22-2-2200-222-2000000000000000020-20-2200000000200000-20-220000000000000
χ4422-2-222222-22-2222-2-2-2-2-2-2-2222-22-22222-222-2-2-2-22-2-2200-222-20000000000000000-20202-200000000-200000202-20000000000000
χ4522-2-222-12-12-22-2-12-2-2-21111-12-12-2-11-21-11112-1-1-121-2-100-11-1100−i3i3−i3−i3i3i300−i3i3−i3−i3i3i3020-2002-20000000-100000100-110000−i3i3−i3i3000
χ4622-2-222-12-12-22-2-12-2-2-21111-12-12-2-11-21-11112-1-1-121-2-100-11-1100−i3i3−i3−i3i3i300−i3i3−i3−i3i3i30-20200-220000000100000-1001-10000i3−i3i3−i3000
χ4722-2-222-12-12-22-2-12-2-2-21111-12-12-2-11-21-11112-1-1-121-2-100-11-1100i3−i3i3i3−i3−i300i3−i3i3i3−i3−i3020-2002-20000000-100000100-110000i3−i3i3−i3000
χ4822-2-222-12-12-22-2-12-2-2-21111-12-12-2-11-21-11112-1-1-121-2-100-11-1100i3−i3i3i3−i3−i300i3−i3i3i3−i3−i30-20200-220000000100000-1001-10000−i3i3−i3i3000
χ4922-2-222-12-12-2-22-1-22-2-21111-12-12-2-112-1-11-1-1-2111-2-12100-111-1003−333−3−300−33−3−333020-200-220000000-1000001001-100003−3−33000
χ5022-2-222-12-12-2-22-1-22-2-21111-12-12-2-112-1-11-1-1-2111-2-12100-111-1003−333−3−300−33−3−3330-202002-20000000100000-100-110000−333−3000
χ5122-2-222-12-12-2-22-1-22-2-21111-12-12-2-112-1-11-1-1-2111-2-12100-111-100−33−3−333003−333−3−3020-200-220000000-1000001001-10000−333−3000
χ5222-2-222-12-12-2-22-1-22-2-21111-12-12-2-112-1-11-1-1-2111-2-12100-111-100−33−3−333003−333−3−30-202002-20000000100000-100-1100003−3−33000
χ5322-2-22-12-12-222-2-1-2211-2-211-1-121-1-221-2-1111-12-1-112-1-2001-11-1−i3i300−i3i3−i3i3−i3i300−i3i3−i3i320-202-200000000-10000010-1100−i3i3−i3i30000000
χ5422-2-22-12-12-222-2-1-2211-2-211-1-121-1-221-2-1111-12-1-112-1-2001-11-1−i3i300−i3i3−i3i3−i3i300−i3i3−i3i3-2020-2200000000100000-101-100i3−i3i3−i30000000
χ5522-2-22-12-12-222-2-1-2211-2-211-1-121-1-221-2-1111-12-1-112-1-2001-11-1i3−i300i3−i3i3−i3i3−i300i3−i3i3−i320-202-200000000-10000010-1100i3−i3i3−i30000000
χ5622-2-22-12-12-222-2-1-2211-2-211-1-121-1-221-2-1111-12-1-112-1-2001-11-1i3−i300i3−i3i3−i3i3−i300i3−i3i3−i3-2020-2200000000100000-101-100−i3i3−i3i30000000
χ5722-2-22-12-12-22-22-12-211-2-211-1-121-1-22-12-11-1-11-211-1-212001-1-113−3003−33−3−3300−33−3320-20-2200000000-100000101-1003−3−330000000
χ5822-2-22-12-12-22-22-12-211-2-211-1-121-1-22-12-11-1-11-211-1-212001-1-113−3003−33−3−3300−33−33-20202-200000000100000-10-1100−333−30000000
χ5922-2-22-12-12-22-22-12-211-2-211-1-121-1-22-12-11-1-11-211-1-212001-1-11−3300−33−333−3003−33−320-20-2200000000-100000101-100−333−30000000
χ6022-2-22-12-12-22-22-12-211-2-211-1-121-1-22-12-11-1-11-211-1-212001-1-11−3300−33−333−3003−33−3-20202-200000000100000-10-11003−3−330000000
χ61444444-24-2-4-444-2-4-444-2-2-2-2-24-2-4-4224-2-2-2-2-24-2-2-2-42-4200222200000000000000000000000000000000000000000000000000000
χ62444444-24-2-4-4-4-4-24444-2-2-2-2-24-2-4-422-42-2-222-42224-24-20022-2-200000000000000000000000000000000000000000000000000000
χ6344444-24-24-4-444-2-4-4-2-244-2-2-2-2422-4-4-24-2-2-2-2-24-2-22-42-400222200000000000000000000000000000000000000000000000000000
χ6444444-24-24-4-4-4-4-244-2-244-2-2-2-2422-4-42-4-2-2222-422-24-240022-2-200000000000000000000000000000000000000000000000000000
χ6544444-2-2-2-24444144-2-2-2-2111-2-2-2-2-2-2-2-21111-2-211-2-2-2-2441111-2-2-2-21111-2-2-2-211110000000000000000000000000000000000000
χ6644444-2-2-2-24444144-2-2-2-2111-2-2-2-2-2-2-2-21111-2-211-2-2-2-2-4-411112222-1-1-1-12222-1-1-1-10000000000000000000000000000000000000
χ6744444-2-2-2-244-4-41-4-4-2-2-2-2111-2-2-2-2-2-22211-1-122-1-122224i−4i11-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000000000000000000000000000000000000
χ6844444-2-2-2-244-4-41-4-4-2-2-2-2111-2-2-2-2-2-22211-1-122-1-12222−4i4i11-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii0000000000000000000000000000000000000
χ6944444-2-2-2-2-4-4441-4-4-2-2-2-2111-2-22222-2-21111-2-211222200-1-1-1-100003-3-3300003-3-330000000000000000000000000000000000000
χ7044444-2-2-2-2-4-4441-4-4-2-2-2-2111-2-22222-2-21111-2-211222200-1-1-1-10000-333-30000-333-30000000000000000000000000000000000000
χ7144444-2-2-2-2-4-4-4-4144-2-2-2-2111-2-222222211-1-122-1-1-2-2-2-200-1-11100003i−3i−3i3i0000−3i3i3i−3i0000000000000000000000000000000000000
χ7244444-2-2-2-2-4-4-4-4144-2-2-2-2111-2-222222211-1-122-1-1-2-2-2-200-1-1110000−3i3i3i−3i00003i−3i−3i3i0000000000000000000000000000000000000
χ73444-4-4444400004004-44-4444-4-4000000-4-400000000000000000000000000000000000000004-4000000000000000000000000000
χ74444-4-4444400004004-44-4444-4-4000000-4-40000000000000000000000000000000000000000-44000000000000000000000000000
χ7544-44-444440000400-44-44-4-44-4-4000000-44000000000000000000000000000000000000000000004-400000000000000000000000
χ7644-44-444440000400-44-44-4-44-4-4000000-4400000000000000000000000000000000000000000000-4400000000000000000000000
χ7744-4-444-24-2-444-4-2-44-4-42222-24-2-442-2-42-22224-2-2-2-4-242002-22-200000000000000000000000000000000000000000000000000000
χ7844-4-444-24-2-44-44-24-4-4-42222-24-2-442-24-2-22-2-2-422242-4-2002-2-2200000000000000000000000000000000000000000000000000000
χ7944-4-44-24-244-44-4-24-422-4-422-2-24-224-42-4-2222-24-2-2-2-42400-22-2200000000000000000000000000000000000000000000000000000
χ8044-4-44-24-244-4-44-2-4422-4-422-2-24-224-4-24-22-2-22-42224-2-400-222-200000000000000000000000000000000000000000000000000000
χ8144-4-44-2-2-2-24-44-414-42222-1-11-2-2-22-22221-1-1-1-2-211-222-2001-11-100−2i32i3i3i3−i3−i300−2i32i3i3i3−i3−i30000000000000000000000000000000000000
χ8244-4-44-2-2-2-24-44-414-42222-1-11-2-2-22-22221-1-1-1-2-211-222-2001-11-1002i3−2i3−i3−i3i3i3002i3−2i3−i3−i3i3i30000000000000000000000000000000000000
χ8344-4-44-2-2-2-24-4-441-442222-1-11-2-2-22-22-2-21-11122-1-12-2-22001-1-110023−23−3−33300−232333−3−30000000000000000000000000000000000000
χ8444-4-44-2-2-2-24-4-441-442222-1-11-2-2-22-22-2-21-11122-1-12-2-22001-1-1100−232333−3−30023−23−3−3330000000000000000000000000000000000000
χ8544-4-44-2-2-2-2-444-41-442222-1-11-2-22-22-2221-1-1-1-2-2112-2-2200-11-11−2i32i300i3−i3i3−i3−2i32i300i3−i3i3−i30000000000000000000000000000000000000
χ8644-4-44-2-2-2-2-444-41-442222-1-11-2-22-22-2221-1-1-1-2-2112-2-2200-11-112i3−2i300−i3i3−i3i32i3−2i300−i3i3−i3i30000000000000000000000000000000000000
χ8744-4-44-2-2-2-2-44-4414-42222-1-11-2-22-22-2-2-21-11122-1-1-222-200-111-123−2300−33−33−2323003−33−30000000000000000000000000000000000000
χ8844-4-44-2-2-2-2-44-4414-42222-1-11-2-22-22-2-2-21-11122-1-1-222-200-111-1−2323003−33−323−2300−33−330000000000000000000000000000000000000
χ89888-8-88-48-40000-4008-8-44-4-4-4-8400000044000000000000000000000000000000000000000000000000000000000000000000000
χ90888-8-8-48-480000-400-448-8-4-4-44-800000044000000000000000000000000000000000000000000000000000000000000000000000
χ91888-8-8-4-4-4-40000200-44-4422244000000-2-26-6006-6000000000000000000000000000000000000000000000000000000000000000
χ92888-8-8-4-4-4-40000200-44-4422244000000-2-2-6600-66000000000000000000000000000000000000000000000000000000000000000
χ9388-88-88-48-40000-400-884-444-4-840000004-4000000000000000000000000000000000000000000000000000000000000000000000
χ9488-88-8-48-480000-4004-4-8844-44-80000004-4000000000000000000000000000000000000000000000000000000000000000000000
χ9588-88-8-4-4-4-400002004-44-4-2-2244000000-226-600-66000000000000000000000000000000000000000000000000000000000000000
χ9688-88-8-4-4-4-400002004-44-4-2-2244000000-22-66006-6000000000000000000000000000000000000000000000000000000000000000
χ978-800088-8-80000800000000-800000000000000000000000000000000000000000000000000004-40000000000000000000000000
χ988-800088-8-80000800000000-80000000000000000000000000000000000000000000000000000-440000000000000000000000000
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).