Finite Group Databasebeta

← Group #72259024

Character table — Group #72259024

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size111122333333336666888888888888888899991818242424242424242424242424242424243232323232323232323232323232323272727272727272727272727272727272
order1222442222222244443366666612121212121212122222446666666612121212121212123366666612121212121212122244444444444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ41111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ511-1-1i−i11-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-1i−i
χ611-1-1i−i11-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-11−ii
χ711-1-1−ii11-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1-1−ii
χ811-1-1−ii11-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-11i−i
χ92222222222222222222-12-12-12-122-1-122-1-122222222-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ10222222222222222222-12-12-12-12-1-122-1-122222222-1-122-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ11222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-12-12-12-122-1-122-1-10000000000000000
χ12222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-12-12-12-1-122-1-1220000000000000000
χ132222-2-222222222-2-2-2-22-12-12-12-1-2-211-2-2112222-2-222-1-122-1-1-2-211-2-211-1-1-1-1-1-1-1-1111111110000000000000000
χ142222-2-222222222-2-2-2-2-12-12-12-1211-2-211-2-22222-2-2-1-122-1-12211-2-211-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ152222-2-222222222-2-2-2-2-1-1-1-1-1-1-1-1111111112222-2-2-1-1-1-1-1-1-1-1111111112-12-12-12-1-2-211-2-2110000000000000000
χ162222-2-222222222-2-2-2-2-1-1-1-1-1-1-1-1111111112222-2-2-1-1-1-1-1-1-1-111111111-12-12-12-1211-2-211-2-20000000000000000
χ1722-2-22i−2i22-2-222-2-22i2i−2i−2i2-12-1-21-212i2i−i−i−2i−2iii2-22-22i−2i22-1-1-2-2112i2i−i−i−2i−2iii-1-1-1-11111−i−i−i−iiiii0000000000000000
χ1822-2-22i−2i22-2-222-2-22i2i−2i−2i-12-121-21-2−i−i2i2iii−2i−2i2-22-22i−2i-1-12211-2-2−i−i2i2iii−2i−2i-1-1-1-11111−i−i−i−iiiii0000000000000000
χ1922-2-22i−2i22-2-222-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii2-22-22i−2i-1-1-1-11111−i−i−i−iiiii2-12-1-21-212i2i−i−i−2i−2iii0000000000000000
χ2022-2-22i−2i22-2-222-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii2-22-22i−2i-1-1-1-11111−i−i−i−iiiii-12-121-21-2−i−i2i2iii−2i−2i0000000000000000
χ2122-2-2−2i2i22-2-222-2-2−2i−2i2i2i2-12-1-21-21−2i−2iii2i2i−i−i2-22-2−2i2i22-1-1-2-211−2i−2iii2i2i−i−i-1-1-1-11111iiii−i−i−i−i0000000000000000
χ2222-2-2−2i2i22-2-222-2-2−2i−2i2i2i-12-121-21-2ii−2i−2i−i−i2i2i2-22-2−2i2i-1-12211-2-2ii−2i−2i−i−i2i2i-1-1-1-11111iiii−i−i−i−i0000000000000000
χ2322-2-2−2i2i22-2-222-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i2-22-2−2i2i-1-1-1-11111iiii−i−i−i−i2-12-1-21-21−2i−2iii2i2i−i−i0000000000000000
χ2422-2-2−2i2i22-2-222-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i2-22-2−2i2i-1-1-1-11111iiii−i−i−i−i-12-121-21-2ii−2i−2i−i−i2i2i0000000000000000
χ252-22-200-2-22222-2-2000022-2-2-2-22200000000-222-2002-22-22-22-20000000022-2-2-2-222000000000000000000000000
χ262-22-200-2-22222-2-200002-1-21-212-100−i3i300−i3i3-222-2002-2-112-2-1100−i3i300−i3i3-1-11111-1-1−i3i3−i3i3−i3i3−i3i30000000000000000
χ272-22-200-2-22222-2-200002-1-21-212-100i3−i300i3−i3-222-2002-2-112-2-1100i3−i300i3−i3-1-11111-1-1i3−i3i3−i3i3−i3i3−i30000000000000000
χ282-22-200-2-22222-2-20000-121-21-2-12−i3i300−i3i300-222-200-112-2-112-2−i3i300−i3i300-1-11111-1-1−i3i3i3−i3−i3i3i3−i30000000000000000
χ292-22-200-2-22222-2-20000-121-21-2-12i3−i300i3−i300-222-200-112-2-112-2i3−i300i3−i300-1-11111-1-1i3−i3−i3i3i3−i3−i3i30000000000000000
χ302-22-200-2-22222-2-20000-1-11111-1-1−i3i3−i3i3−i3i3−i3i3-222-200-11-11-11-11−i3i3−i3i3−i3i3−i3i3-121-21-2-12i3−i300i3−i3000000000000000000
χ312-22-200-2-22222-2-20000-1-11111-1-1−i3i3i3−i3−i3i3i3−i3-222-200-11-11-11-11−i3i3i3−i3−i3i3i3−i32-1-21-212-100−i3i300−i3i30000000000000000
χ322-22-200-2-22222-2-20000-1-11111-1-1i3−i3−i3i3i3−i3−i3i3-222-200-11-11-11-11i3−i3−i3i3i3−i3−i3i32-1-21-212-100i3−i300i3−i30000000000000000
χ332-22-200-2-22222-2-20000-1-11111-1-1i3−i3i3−i3i3−i3i3−i3-222-200-11-11-11-11i3−i3i3−i3i3−i3i3−i3-121-21-2-12−i3i300−i3i3000000000000000000
χ342-2-2200-2-2-2-22222000022-2-222-2-200000000-2-222002-22-2-22-220000000022-2-222-2-2000000000000000000000000
χ352-2-2200-2-2-2-2222200002-1-212-1-21003−300−33-2-222002-2-11-221-1003−300−33-1-111-1-1113−33−3−33−330000000000000000
χ362-2-2200-2-2-2-2222200002-1-212-1-2100−33003−3-2-222002-2-11-221-100−33003−3-1-111-1-111−33−333−33−30000000000000000
χ372-2-2200-2-2-2-222220000-121-2-121-23−300−3300-2-22200-112-21-1-223−300−3300-1-111-1-1113−3−33−333−30000000000000000
χ382-2-2200-2-2-2-222220000-121-2-121-2−33003−300-2-22200-112-21-1-22−33003−300-1-111-1-111−333−33−3−330000000000000000
χ392-2-2200-2-2-2-222220000-1-111-1-1113−33−3−33−33-2-22200-11-111-11-13−33−3−33−33-121-2-121-2−33003−3000000000000000000
χ402-2-2200-2-2-2-222220000-1-111-1-1113−3−33−333−3-2-22200-11-111-11-13−3−33−333−32-1-212-1-21003−300−330000000000000000
χ412-2-2200-2-2-2-222220000-1-111-1-111−333−33−3−33-2-22200-11-111-11-1−333−33−3−332-1-212-1-2100−33003−30000000000000000
χ422-2-2200-2-2-2-222220000-1-111-1-111−33−333−33−3-2-22200-11-111-11-1−33−333−33−3-121-2-121-23−300−33000000000000000000
χ433333333-13-13-13-13-13-10303030300330033-1-1-1-1-1-100-1-100-1-100-1-100-1-1000000000000000011111-11-11-11-1-1-1-1-1
χ443333333-13-13-13-13-13-10303030300330033-1-1-1-1-1-100-1-100-1-100-1-100-1-10000000000000000-1-1-1-1-11-11-11-111111
χ45333333-13-13-13-13-13-133030303033003300-1-1-1-1-1-1-1-100-1-100-1-100-1-10000000000000000001111-11-11-11-11-1-1-1-1
χ46333333-13-13-13-13-13-133030303033003300-1-1-1-1-1-1-1-100-1-100-1-100-1-1000000000000000000-1-1-1-11-11-11-11-11111
χ473333-3-33-13-13-13-1-31-310303030300-3-300-3-3-1-1-1-11100-1-100-1-100110011000000000000000011-1-11-11-1-11-11-1-111
χ483333-3-33-13-13-13-1-31-310303030300-3-300-3-3-1-1-1-11100-1-100-1-1001100110000000000000000-1-111-11-111-11-111-1-1
χ493333-3-3-13-13-13-131-31-330303030-3-300-3-300-1-1-1-111-1-100-1-10011001100000000000000000011-1-1-11-111-11-1-1-111
χ503333-3-3-13-13-13-131-31-330303030-3-300-3-300-1-1-1-111-1-100-1-100110011000000000000000000-1-1111-11-1-11-1111-1-1
χ5133-3-33i−3i3-1-313-1-313i−i−3ii03030-30-3003i3i00−3i−3i-11-11−ii00-1-1001100−i−i00ii00000000000000001-1i−i1-1-11i−i−ii-11−ii
χ5233-3-33i−3i3-1-313-1-313i−i−3ii03030-30-3003i3i00−3i−3i-11-11−ii00-1-1001100−i−i00ii0000000000000000-11−ii-111-1−iii−i1-1i−i
χ5333-3-33i−3i-131-3-131-3−i3ii−3i3030-30-303i3i00−3i−3i00-11-11−ii-1-1001100−i−i00ii0000000000000000001-1i−i-111-1−iii−i-11−ii
χ5433-3-33i−3i-131-3-131-3−i3ii−3i3030-30-303i3i00−3i−3i00-11-11−ii-1-1001100−i−i00ii000000000000000000-11−ii1-1-11i−i−ii1-1i−i
χ5533-3-3−3i3i3-1-313-1-31−3ii3i−i03030-30-300−3i−3i003i3i-11-11i−i00-1-1001100ii00−i−i00000000000000001-1−ii1-1-11−iii−i-11i−i
χ5633-3-3−3i3i3-1-313-1-31−3ii3i−i03030-30-300−3i−3i003i3i-11-11i−i00-1-1001100ii00−i−i0000000000000000-11i−i-111-1i−i−ii1-1−ii
χ5733-3-3−3i3i-131-3-131-3i−3i−i3i3030-30-30−3i−3i003i3i00-11-11i−i-1-1001100ii00−i−i0000000000000000001-1−ii-111-1i−i−ii-11i−i
χ5833-3-3−3i3i-131-3-131-3i−3i−i3i3030-30-30−3i−3i003i3i00-11-11i−i-1-1001100ii00−i−i000000000000000000-11i−i1-1-11−iii−i1-1−ii
χ596666666-26-26-26-26-26-20-30-30-30-300-3-300-3-3-2-2-2-2-2-2001100110011001100000000000000000000000000000000
χ60666666-26-26-26-26-26-26-30-30-30-30-3-300-3-300-2-2-2-2-2-2110011001100110000000000000000000000000000000000
χ616666-6-66-26-26-26-2-62-620-30-30-30-300330033-2-2-2-2220011001100-1-100-1-100000000000000000000000000000000
χ626666-6-6-26-26-26-262-62-6-30-30-30-3033003300-2-2-2-22211001100-1-100-1-10000000000000000000000000000000000
χ6366-6-66i−6i6-2-626-2-626i−2i−6i2i0-30-3030300−3i−3i003i3i-22-22−2i2i001100-1-100ii00−i−i00000000000000000000000000000000
χ6466-6-66i−6i-262-6-262-6−2i6i2i−6i-30-303030−3i−3i003i3i00-22-22−2i2i1100-1-100ii00−i−i0000000000000000000000000000000000
χ6566-6-6−6i6i6-2-626-2-62−6i2i6i−2i0-30-30303003i3i00−3i−3i-22-222i−2i001100-1-100−i−i00ii00000000000000000000000000000000
χ6666-6-6−6i6i-262-6-262-62i−6i−2i6i-30-3030303i3i00−3i−3i00-22-222i−2i1100-1-100−i−i00ii0000000000000000000000000000000000
χ676-66-6002-6-26-262-6000060-60-6060000000002-2-2200-2200-22000000000000000000000000000000000000000000
χ686-66-6002-6-26-262-60000-303030-30−3i33i300−3i33i3002-2-22001-1001-100i3−i300i3−i30000000000000000000000000000000000
χ696-66-6002-6-26-262-60000-303030-303i3−3i3003i3−3i3002-2-22001-1001-100−i3i300−i3i30000000000000000000000000000000000
χ706-66-600-626-26-2-620000060-60-606000000002-2-220000-2200-220000000000000000000000000000000000000000
χ716-66-600-626-26-2-6200000-303030-300−3i33i300−3i33i32-2-2200001-1001-100i3−i300i3−i300000000000000000000000000000000
χ726-66-600-626-26-2-6200000-303030-3003i3−3i3003i3−3i32-2-2200001-1001-100−i3i300−i3i300000000000000000000000000000000
χ736-6-66002-62-6-26-26000060-6060-600000000022-2-200-22002-2000000000000000000000000000000000000000000
χ746-6-66002-62-6-26-260000-3030-303033−3300−33330022-2-2001-100-1100−33003−30000000000000000000000000000000000
χ756-6-66002-62-6-26-260000-3030-3030−33330033−330022-2-2001-100-11003−300−330000000000000000000000000000000000
χ766-6-6600-62-626-26-20000060-6060-60000000022-2-20000-22002-20000000000000000000000000000000000000000
χ776-6-6600-62-626-26-200000-3030-3030033−3300−333322-2-200001-100-1100−33003−300000000000000000000000000000000
χ786-6-6600-62-626-26-200000-3030-30300−33330033−3322-2-200001-100-11003−300−3300000000000000000000000000000000
χ79999999-3-3-3-3-3-3-3-3-3-3-3-30000000000000000111111000000000000000000000000000000001111-1-1-1-1-1-1-1-11111
χ80999999-3-3-3-3-3-3-3-3-3-3-3-3000000000000000011111100000000000000000000000000000000-1-1-1-111111111-1-1-1-1
χ819999-9-9-3-3-3-3-3-3-3-3333300000000000000001111-1-10000000000000000000000000000000011-1-1-1-1-1-1111111-1-1
χ829999-9-9-3-3-3-3-3-3-3-3333300000000000000001111-1-100000000000000000000000000000000-1-1111111-1-1-1-1-1-111
χ8399-9-99i−9i-3-333-3-333−3i−3i3i3i00000000000000001-11-1i−i000000000000000000000000000000001-1i−i-1-111−i−iii1-1i−i
χ8499-9-99i−9i-3-333-3-333−3i−3i3i3i00000000000000001-11-1i−i00000000000000000000000000000000-11−ii11-1-1ii−i−i-11−ii
χ8599-9-9−9i9i-3-333-3-3333i3i−3i−3i00000000000000001-11-1−ii000000000000000000000000000000001-1−ii-1-111ii−i−i1-1−ii
χ8699-9-9−9i9i-3-333-3-3333i3i−3i−3i00000000000000001-11-1−ii00000000000000000000000000000000-11i−i11-1-1−i−iii-11i−i
χ8718-1818-180066-6-6-6-66600000000000000000000-222-200000000000000000000000000000000000000000000000000
χ8818-18-1818006666-6-6-6-600000000000000000000-2-22200000000000000000000000000000000000000000000000000

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