Finite Group Databasebeta

← Group #13172123

Character table — Group #13172123

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222244444444444444466888888888888888812121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363654547272108
order1222333666666666233366666666666443666666666666666224446666121212124444444466666612121212121212121212121212124412121212121212122212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-111-1-11111-1-1-1-111-1-11-111-1-1111-11-1111111-1-11-111-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-111-11-1-1111111-1-1-1-1-1-111-11-1-11111-11-111111-1-111-11-1-111-1-1-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-1111111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-11-11-1-1-1-1-111-1-1-11-1-111-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-111-1-1-1-1-1-1-1-111-1-1-11-1-111-1-1-11-11-1-1-1-1-1-1111-111-1-1-1-1-1-1111-11
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-11111111111-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1111-1-11111-1-11111-1-11-111-1-1-1-1-11-1111-1-1-1-111-1111-1-1-1-11111-11-1
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1-1-1111111-1-111-1-111-11-1-111-1-11-11-111-1-111-1-11-1-1-111-1-111111-1-1
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-111-1-1-1-1111
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-11-1111-1-1-1-1-1-1-1-111-1-1111-111-1-111-11-11-1-111-1-1111-1-1-111-1-111-1-11-11
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-111-1-1-1-1-1-11111-1-1-11-1-111111-11-1-1-11111-1-1-1111-1-1-1-111-1-1-111
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1111111-1-1111111-1-111-1-1-1
χ17222222-1-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-1220222222000022220000-1-1-1-1-1-100-1-1220000-1-1-1-1000000-1-1-1-100000
χ18222222-1-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-12-202-222-2-20000-2-2-2-20000-11-1-11100-112-20000-1-111000000111100000
χ19222222-1-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-220-22-2-2220000-2-2-2-200001-111-1-1001-1-22000011-1-1000000111100000
χ20222222-1-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-2-2-20000222200001111110011-2-200001111000000-1-1-1-100000
χ21222222-1-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-11111220-2-22222000022-2-20000-1-1-1-1-1-10011-2-200001111000000-1-11100000
χ22222222-1-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-111112-20-2222-2-20000-2-2220000-11-1-111001-1-22000011-1-100000011-1-100000
χ23222222-1-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-11111-2202-2-2-2220000-2-22200001-111-1-100-112-20000-1-11100000011-1-100000
χ24222222-1-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-11111-2-2022-2-2-2-2000022-2-2000011111100-1-1220000-1-1-1-1000000-1-11100000
χ2522222-1222-122-12-122-12-122-122-1-1-1-12-122-12-1-1-122-1-1-1-1-1-1-1-1-10220200-1-122-1-1000000220200-1-12-1020-1-1-1-1-100-1-10200-1-10000000-10
χ2622222-1222-122-12-122-12-122-122-1-1-1-12-122-12-1-1-122-1-1-1-1-1-1-1-1-10-220-2001122-1-1000000-2-20-200112-10-201-1-1-1-100110-20011000000010
χ2722222-1222-122-12-122-12-122-122-1-1-1-12-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-102-20200-1-1-2-211000000-2-20200-1-1-21020-1111100-1-10-20011000000010
χ2822222-1222-122-12-122-12-122-122-1-1-1-12-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-10-2-20-20011-2-211000000220-20011-210-201111100110200-1-10000000-10
χ2922222-1222-122-12-12-2-12-1-2-2-122-1-1-1-12-122-1-2111-2-211-1-1-1111102-20-200-1-122-1-1000000220200-1-1-210-201-1-11100110-200-1-1000000010
χ3022222-1222-122-12-12-2-12-1-2-2-122-1-1-1-12-122-1-2111-2-211-1-1-111110-2-202001122-1-1000000-2-20-20011-21020-1-1-11100-1-10200110000000-10
χ3122222-1222-122-12-12-2-12-1-2-2-122-1-1-1-12-1-2-2-1-2111-2-211-1-1-111110220-200-1-1-2-211000000-2-20200-1-12-10-20111-1-100110200110000000-10
χ3222222-1222-122-12-12-2-12-1-2-2-122-1-1-1-12-1-2-2-1-2111-2-211-1-1-111110-22020011-2-211000000220-200112-1020-111-1-100-1-10-200-1-1000000010
χ332222-1222-122-12-1222-1-1222-1-1-122-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-120220-1-100-1-1220000220020-1-100-1220-10-1-1-1-1-1-10020-1-100000000-100
χ342222-1222-122-12-1222-1-1222-1-1-122-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-1-202-201100-1-1220000-2-200-201100-12-2010-1-1-1-11100-201100000000100
χ352222-1222-122-12-1222-1-1222-1-1-122-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-120-220-1-10011-2-20000-2-20020-1-1001-220-101111-1-100-201100000000100
χ362222-1222-122-12-1222-1-1222-1-1-122-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-1-20-2-20110011-2-200002200-2011001-2-20101111110020-1-100000000-100
χ372222-1222-122-12-122-2-1-12-2-2-1-1-122-1-1-1222-11-21111-2-2-1-1-1111120-2-20-1-100-1-1220000220020-1-1001-2-2010-1-1111100-20-1-100000000100
χ382222-1222-122-12-122-2-1-12-2-2-1-1-122-1-1-1222-11-21111-2-2-1-1-11111-20-2201100-1-1220000-2-200-2011001-220-10-1-111-1-100201100000000-100
χ392222-1222-122-12-122-2-1-12-2-2-1-1-122-1-1-12-2-2-11-21111-2-2-1-1-11111202-20-1-10011-2-20000-2-20020-1-100-12-201011-1-11100201100000000-100
χ402222-1222-122-12-122-2-1-12-2-2-1-1-122-1-1-12-2-2-11-21111-2-2-1-1-11111-20220110011-2-200002200-201100-1220-1011-1-1-1-100-20-1-100000000100
χ4122-2-2222-222-2-2-2-2-22022200-22-22-22-2-2-2002000000002-2-2000000000000000002-2002i−2i2i−2i00000000000000000000002i−2i2i−2i2-20000000
χ4222-2-2222-222-2-2-2-2-22022200-22-22-22-2-2-2002000000002-2-2000000000000000002-200−2i2i−2i2i0000000000000000000000−2i2i−2i2i2-20000000
χ4322-2-2222-222-2-2-2-2-22022200-22-22-22-2-2-2002000000002-2-200000000000000000-22002i−2i−2i2i00000000000000000000002i−2i−2i2i-220000000
χ4422-2-2222-222-2-2-2-2-22022200-22-22-22-2-2-2002000000002-2-200000000000000000-2200−2i2i2i−2i0000000000000000000000−2i2i2i−2i-220000000
χ452-2-222222-2-2-222-2-2-20222002-22-22-2-2-2-22i−2i200000000-22-200000000000002i−2i2i−2i002i−2i00000000000000002i−2i000000000000002i−2i2-2000
χ462-2-222222-2-2-222-2-2-20222002-22-22-2-2-2-22i−2i200000000-22-200000000000002i−2i2i−2i00−2i2i00000000000000002i−2i00000000000000−2i2i-22000
χ472-2-222222-2-2-222-2-2-20222002-22-22-2-2-2-2−2i2i200000000-22-20000000000000−2i2i−2i2i002i−2i0000000000000000−2i2i000000000000002i−2i-22000
χ482-2-222222-2-2-222-2-2-20222002-22-22-2-2-2-2−2i2i200000000-22-20000000000000−2i2i−2i2i00−2i2i0000000000000000−2i2i00000000000000−2i2i2-2000
χ4944444-2-2-24-2-24-24-2-24-2-21-2-2-2-2-211-2-2-210014-2-2-2-2-21111111110400400-2-20000000000000-20011000-20-200000011000000000000000
χ5044444-2-2-24-2-24-24-2-24-2-21-2-2-2-2-211-2-2-210014-2-2-2-2-21111111110-400-400220000000000000200-1-1000202000000-1-1000000000000000
χ5144444-2-2-24-2-24-24-2-2-4-2-2122-2-2-211-2-2-21001-422222-1-1111-1-1-1-10400-400-2-20000000000000-20011000202000000-1-1000000000000000
χ5244444-2-2-24-2-24-24-2-2-4-2-2122-2-2-211-2-2-21001-422222-1-1111-1-1-1-10-400400220000000000000200-1-1000-20-200000011000000000000000
χ534444-24-2-2-24-2-24-24-24-21-2-2-2-211-2-2-2-21-2001-24-2-211-2-2111111140040-2-200000000000000-20110000-20-2000001100000000000000000
χ544444-24-2-2-24-2-24-24-24-21-2-2-2-211-2-2-2-21-2001-24-2-211-2-21111111-400-40220000000000000020-1-1000020200000-1-100000000000000000
χ554444-24-2-2-24-2-24-24-2-4-21-222-211-2-2-2-21-20012-422-1-122111-1-1-1-1400-40-2-200000000000000-2011000020200000-1-100000000000000000
χ564444-24-2-2-24-2-24-24-2-4-21-222-211-2-2-2-21-20012-422-1-122111-1-1-1-1-40040220000000000000020-1-10000-20-2000001100000000000000000
χ574444-2-244-2-24-2-2-2-2441-2-2441-2-2-2-211-2-2441-2-211-2-2-2-21111111004000000-2-2-2-200000000000000-2-2000011110000000000000000000
χ584444-2-244-2-24-2-2-2-2441-2-2441-2-2-2-211-2-2-4-41-2-211-2-2-2-2111111100-4000000222200000000000000220000-1-1-1-10000000000000000000
χ594444-2-244-2-24-2-2-2-24-41-2-2-4-41-2-2-2-211-2-244122-1-12222111-1-1-1-100-4000000-2-2-2-20000000000000022000011-1-10000000000000000000
χ604444-2-244-2-24-2-2-2-24-41-2-2-4-41-2-2-2-211-2-2-4-4122-1-12222111-1-1-1-1004000000222200000000000000-2-20000-1-1110000000000000000000
χ6144-4-444-22442-4-4-4-4-204-2-200-4-22-224-42200-200000000-222000000000000000004-400000000000000000000000000000000-220000000
χ6244-4-444-22442-4-4-4-4-204-2-200-4-22-224-42200-200000000-22200000000000000000-44000000000000000000000000000000002-20000000
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χ998-88-8-4-48-844844-4-4-802-4-400-24444-22-4-400200000000-2-22000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-4444-444-4-440222−4i34i3-2-2-2-2-2-222200-100002i3−2i32i3−2i311-1−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-4444-444-4-4402224i3−4i3-2-2-2-2-2-222200-10000−2i32i3−2i32i311-1i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ1028-8-888-4-4-4-8448-4-8440-4-4200-44-4-22444-200200000000-22-2000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-48-4-44-84-484-840-42-400-4-224-444-2400200000000-22-2000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-4-4444-4-44440222002-22-22-2-2-2-200-1006-600001-11-33-3300000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4-4444-4-44440222002-22-22-2-2-2-200-100-6600001-113-33-300000000000000000000000000000000000000000000000000000000

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