Finite Group Databasebeta

← Group #13152072

Character table — Group #13152072

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222444666666661212121212121212121212121818181818183636363636363636363636363636361111222244466666666121212121212121212121212181818181818363636363636363636363636363636
order1222366626633666666366666666666224444444661212121212121212121222226666266666666666666666666662244444446612121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111-1-111-1-11-1-1-1-11111-1-1-1-1-1-11111111111111111111111111111111-1-111-1-11-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111-11-1-1-1-1-1-1-1-1-111111111111111111111111111111111111-1-1-1-111-11-1-1-1-1-1-1-1-1-11111
χ511111111-1-1-1111111111-1-1-1-1111-1-1-1-1111111-1-1-11111-1-1-1-111-1-111111111-1-1-1111111111-1-1-1-1111-1-1-1-1111111-1-1-11111-1-1-1-111-1-1
χ611111111-1-1-1111111111-1-1-1-1111-1-1-1-111-1-1-1-111-111-1-111-1-1-1-11111111111-1-1-1111111111-1-1-1-1111-1-1-1-111-1-1-1-111-111-1-111-1-1-1-111
χ711111111-1-1-1111111111-1-1-1-1111-1-1-1-1-1-111-1-1-111-1-111-1-111-1-11111111111-1-1-1111111111-1-1-1-1111-1-1-1-1-1-111-1-1-111-1-111-1-111-1-111
χ811111111-1-1-1111111111-1-1-1-1111-1-1-1-1-1-1-1-1111-11-1-1-1-1111111-1-111111111-1-1-1111111111-1-1-1-1111-1-1-1-1-1-1-1-1111-11-1-1-1-1111111-1-1
χ9222222222222-12-1-122-1-122-1-1-1-1-1-1-1-1-1220000002-1-10000-1-10000222222222222-12-1-122-1-122-1-1-1-1-1-1-1-1-1220000002-1-10000-1-10000
χ10222222222222-12-1-122-1-122-1-1-1-1-1-1-1-1-1-2-2000000-2110000110000222222222222-12-1-122-1-122-1-1-1-1-1-1-1-1-1-2-2000000-2110000110000
χ1122222222222-12-122-1-12-1-1-122-1-1-1-1-1-1-100002202000000000-1-1-1-122222222222-12-122-1-12-1-1-122-1-1-1-1-1-1-100002202000000000-1-1-1-1
χ1222222222222-12-122-1-12-1-1-122-1-1-1-1-1-1-10000-2-20-2000000000111122222222222-12-122-1-12-1-1-122-1-1-1-1-1-1-10000-2-20-20000000001111
χ1322222222-2-2-22-12-1-122-1-1-2-211-1-1-1111122000000-2-1-1000011000022222222-2-2-22-12-1-122-1-1-2-211-1-1-1111122000000-2-1-10000110000
χ1422222222-2-2-22-12-1-122-1-1-2-211-1-1-11111-2-20000002110000-1-1000022222222-2-2-22-12-1-122-1-1-2-211-1-1-11111-2-20000002110000-1-10000
χ1522222222-2-2-2-12-122-1-12-111-2-2-1-1-111110000220-2000000000-1-11122222222-2-2-2-12-122-1-12-111-2-2-1-1-111110000220-2000000000-1-111
χ1622222222-2-2-2-12-122-1-12-111-2-2-1-1-111110000-2-20200000000011-1-122222222-2-2-2-12-122-1-12-111-2-2-1-1-111110000-2-20200000000011-1-1
χ1722-2-222-2-200022-22-22-2-2200002-2-20000002i−2i00000002i−2i0000000022-2-222-2-200022-22-22-2-2200002-2-20000002i−2i00000002i−2i00000000
χ1822-2-222-2-200022-22-22-2-2200002-2-2000000−2i2i0000000−2i2i0000000022-2-222-2-200022-22-22-2-2200002-2-2000000−2i2i0000000−2i2i00000000
χ192-22-22-22-2000222-22-2-2-220000-22-2000000002i−2i000000000002i−2i002-22-22-22-2000222-22-2-2-220000-22-2000000002i−2i000000000002i−2i00
χ202-22-22-22-2000222-22-2-2-220000-22-200000000−2i2i00000000000−2i2i002-22-22-22-2000222-22-2-2-220000-22-200000000−2i2i00000000000−2i2i00
χ212-22-22-22-2000-12-1-2211-2-1−i3i3001-11−i3−i3i3i300002i−2i00000000000−ii3−32-22-22-22-2000-12-1-2211-2-1−i3i3001-11−i3−i3i3i300002i−2i00000000000−ii3−3
χ222-22-22-22-2000-12-1-2211-2-1−i3i3001-11−i3−i3i3i30000−2i2i00000000000i−i−332-22-22-22-2000-12-1-2211-2-1−i3i3001-11−i3−i3i3i30000−2i2i00000000000i−i−33
χ232-22-22-22-2000-12-1-2211-2-1i3−i3001-11i3i3−i3−i300002i−2i00000000000−ii−332-22-22-22-2000-12-1-2211-2-1i3−i3001-11i3i3−i3−i300002i−2i00000000000−ii−33
χ242-22-22-22-2000-12-1-2211-2-1i3−i3001-11i3i3−i3−i30000−2i2i00000000000i−i3−32-22-22-22-2000-12-1-2211-2-1i3−i3001-11i3i3−i3−i30000−2i2i00000000000i−i3−3
χ252-2-222-2-2200022-2-2-2-22220000-2-2200002-200000002-200000000002-2-222-2-2200022-2-2-2-22220000-2-2200002-200000002-20000000000
χ262-2-222-2-2200022-2-2-2-22220000-2-220000-220000000-2200000000002-2-222-2-2200022-2-2-2-22220000-2-220000-220000000-220000000000
χ272-2-222-2-220002-1-211-22-1-100−i3i311-1−i3i3−i3i32-20000000-110000−i3i300002-2-222-2-220002-1-211-22-1-100−i3i311-1−i3i3−i3i32-20000000-110000−i3i30000
χ282-2-222-2-220002-1-211-22-1-100−i3i311-1−i3i3−i3i3-2200000001-10000i3−i300002-2-222-2-220002-1-211-22-1-100−i3i311-1−i3i3−i3i3-2200000001-10000i3−i30000
χ292-2-222-2-220002-1-211-22-1-100i3−i311-1i3−i3i3−i32-20000000-110000i3−i300002-2-222-2-220002-1-211-22-1-100i3−i311-1i3−i3i3−i32-20000000-110000i3−i30000
χ302-2-222-2-220002-1-211-22-1-100i3−i311-1i3−i3i3−i3-2200000001-10000−i3i300002-2-222-2-220002-1-211-22-1-100i3−i311-1i3−i3i3−i3-2200000001-10000−i3i30000
χ3144444444444-2-2-2-2-2-2-2-21-2-2-2-2111111100000000000000000000044444444444-2-2-2-2-2-2-2-21-2-2-2-21111111000000000000000000000
χ3244444444-4-4-4-2-2-2-2-2-2-2-212222111-1-1-1-100000000000000000000044444444-4-4-4-2-2-2-2-2-2-2-212222111-1-1-1-1000000000000000000000
χ3344-4-444-4-40004-2-4-224-42-20000-222000000000000000000000000044-4-444-4-40004-2-4-224-42-20000-2220000000000000000000000000
χ3444-4-444-4-4000-2424-4-22-4-20000-222000000000000000000000000044-4-444-4-4000-2424-4-22-4-20000-2220000000000000000000000000
χ3544-4-444-4-4000-2-22-22-222100001-1-13-3-3300000000000000000000044-4-444-4-4000-2-22-22-222100001-1-13-3-33000000000000000000000
χ3644-4-444-4-4000-2-22-22-222100001-1-1-333-300000000000000000000044-4-444-4-4000-2-22-22-222100001-1-1-333-3000000000000000000000
χ374-44-44-44-40004-242-2-4-42-200002-2200000000000000000000000004-44-44-44-40004-242-2-4-42-200002-220000000000000000000000000
χ384-44-44-44-4000-2-2-22-22221−2i32i300-11-1i3i3−i3−i30000000000000000000004-44-44-44-4000-2-2-22-22221−2i32i300-11-1i3i3−i3−i3000000000000000000000
χ394-44-44-44-4000-2-2-22-222212i3−2i300-11-1−i3−i3i3i30000000000000000000004-44-44-44-4000-2-2-22-222212i3−2i300-11-1−i3−i3i3i3000000000000000000000
χ404-4-444-4-44000-242-4-42-24-2000022-200000000000000000000000004-4-444-4-44000-242-4-42-24-2000022-20000000000000000000000000
χ414-4-444-4-44000-2-22222-2-2100−2i32i3-1-11i3−i3i3−i30000000000000000000004-4-444-4-44000-2-22222-2-2100−2i32i3-1-11i3−i3i3−i3000000000000000000000
χ424-4-444-4-44000-2-22222-2-21002i3−2i3-1-11−i3i3−i3i30000000000000000000004-4-444-4-44000-2-22222-2-21002i3−2i3-1-11−i3i3−i3i3000000000000000000000
χ436666-3-3-3-36-3-30000000000000000000000220020000-1-1-1-10000006666-3-3-3-36-3-30000000000000000000000220020000-1-1-1-1000000
χ446666-3-3-3-36-3-30000000000000000000000-2-200-2000011110000006666-3-3-3-36-3-30000000000000000000000-2-200-200001111000000
χ456666-3-3-3-3-63300000000000000000000002200-20000-1-1110000006666-3-3-3-3-63300000000000000000000002200-20000-1-111000000
χ466666-3-3-3-3-6330000000000000000000000-2-2002000011-1-10000006666-3-3-3-3-6330000000000000000000000-2-2002000011-1-1000000
χ4766-6-6-3-3330−3i33i300000000000000000000002i−2i0000000−ii3−300000066-6-6-3-3330−3i33i300000000000000000000002i−2i0000000−ii3−3000000
χ4866-6-6-3-3330−3i33i30000000000000000000000−2i2i0000000i−i−3300000066-6-6-3-3330−3i33i30000000000000000000000−2i2i0000000i−i−33000000
χ4966-6-6-3-33303i3−3i300000000000000000000002i−2i0000000−ii−3300000066-6-6-3-33303i3−3i300000000000000000000002i−2i0000000−ii−33000000
χ5066-6-6-3-33303i3−3i30000000000000000000000−2i2i0000000i−i3−300000066-6-6-3-33303i3−3i30000000000000000000000−2i2i0000000i−i3−3000000
χ5112-1212-12-66-660000000000000000000000000000000000000000000012-1212-12-66-6600000000000000000000000000000000000000000000
χ5212-12-1212-666-60000000000000000000000000000000000000000000012-12-1212-666-600000000000000000000000000000000000000000000
χ531111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ54111111111111111111111111111111111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-11111
χ551111111111111111111111111111111-1-111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11111-1-1-1-1111111
χ561111111111111111111111111111111-1-1-1-111-11-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1111111111-1-1-1-1
χ5711111111-1-1-1111111111-1-1-1-1111-1-1-1-1111111-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1111-1-1-1-11111-1-111
χ5811111111-1-1-1111111111-1-1-1-1111-1-1-1-111-1-1-1-111-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-1-11111-1-11111-1-11-1-111-1-11111-1-1
χ5911111111-1-1-1111111111-1-1-1-1111-1-1-1-1-1-111-1-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-1-1111111-1-1111-1-111-1-111-1-111-1-1
χ6011111111-1-1-1111111111-1-1-1-1111-1-1-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-1-111111111-1-1-11-11111-1-1-1-1-1-111
χ61222222222222-12-1-122-1-122-1-1-1-1-1-1-1-1-1220000002-1-10000-1-10000-2-2-2-2-2-2-2-2-2-2-2-21-211-2-211-2-2111111111-2-2000000-2110000110000
χ62222222222222-12-1-122-1-122-1-1-1-1-1-1-1-1-1-2-2000000-2110000110000-2-2-2-2-2-2-2-2-2-2-2-21-211-2-211-2-2111111111220000002-1-10000-1-10000
χ6322222222222-12-122-1-12-1-1-122-1-1-1-1-1-1-100002202000000000-1-1-1-1-2-2-2-2-2-2-2-2-2-2-21-21-2-211-2111-2-211111110000-2-20-20000000001111
χ6422222222222-12-122-1-12-1-1-122-1-1-1-1-1-1-10000-2-20-20000000001111-2-2-2-2-2-2-2-2-2-2-21-21-2-211-2111-2-2111111100002202000000000-1-1-1-1
χ6522222222-2-2-22-12-1-122-1-1-2-211-1-1-1111122000000-2-1-10000110000-2-2-2-2-2-2-2-2222-21-211-2-21122-1-1111-1-1-1-1-2-20000002110000-1-10000
χ6622222222-2-2-22-12-1-122-1-1-2-211-1-1-11111-2-20000002110000-1-10000-2-2-2-2-2-2-2-2222-21-211-2-21122-1-1111-1-1-1-122000000-2-1-10000110000
χ6722222222-2-2-2-12-122-1-12-111-2-2-1-1-111110000220-2000000000-1-111-2-2-2-2-2-2-2-22221-21-2-211-21-1-122111-1-1-1-10000-2-20200000000011-1-1
χ6822222222-2-2-2-12-122-1-12-111-2-2-1-1-111110000-2-20200000000011-1-1-2-2-2-2-2-2-2-22221-21-2-211-21-1-122111-1-1-1-10000220-2000000000-1-111
χ6922-2-222-2-200022-22-22-2-2200002-2-20000002i−2i00000002i−2i00000000-2-222-2-222000-2-22-22-222-20000-222000000−2i2i0000000−2i2i00000000
χ7022-2-222-2-200022-22-22-2-2200002-2-2000000−2i2i0000000−2i2i00000000-2-222-2-222000-2-22-22-222-20000-2220000002i−2i00000002i−2i00000000
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χ956666-3-3-3-36-3-30000000000000000000000220020000-1-1-1-1000000-6-6-6-63333-6330000000000000000000000-2-200-200001111000000
χ966666-3-3-3-36-3-30000000000000000000000-2-200-200001111000000-6-6-6-63333-6330000000000000000000000220020000-1-1-1-1000000
χ976666-3-3-3-3-63300000000000000000000002200-20000-1-111000000-6-6-6-633336-3-30000000000000000000000-2-2002000011-1-1000000
χ986666-3-3-3-3-6330000000000000000000000-2-2002000011-1-1000000-6-6-6-633336-3-300000000000000000000002200-20000-1-111000000
χ9966-6-6-3-3330−3i33i300000000000000000000002i−2i0000000−ii3−3000000-6-66633-3-303i3−3i30000000000000000000000−2i2i0000000i−i−33000000
χ10066-6-6-3-3330−3i33i30000000000000000000000−2i2i0000000i−i−33000000-6-66633-3-303i3−3i300000000000000000000002i−2i0000000−ii3−3000000
χ10166-6-6-3-33303i3−3i300000000000000000000002i−2i0000000−ii−33000000-6-66633-3-30−3i33i30000000000000000000000−2i2i0000000i−i3−3000000
χ10266-6-6-3-33303i3−3i30000000000000000000000−2i2i0000000i−i3−3000000-6-66633-3-30−3i33i300000000000000000000002i−2i0000000−ii−33000000
χ10312-1212-12-66-6600000000000000000000000000000000000000000000-1212-12126-66-600000000000000000000000000000000000000000000
χ10412-12-1212-666-600000000000000000000000000000000000000000000-121212-126-6-6600000000000000000000000000000000000000000000

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