Finite Group Databasebeta

← Group #72241521

Character table — Group #72241521

Order 3456.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11223333666688889916161616181818181818181818182424242436363636363636364848484854545454545454546464646464647272727272727272144144144144144144144144
order12362222666633662233664444444466666622444444666644444444333666661212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1
χ31111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ41111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ51-11-111-1-1-1-11111-1-1-1111-1-1i−ii−ii−ii−i-1111-1-11-111-1-11-111-1-1i−ii−ii−ii−i111-1-1-11-111-1-11-1i−ii−ii−ii−i
χ61-11-111-1-1-1-11111-1-1-1111-1-1i−i−iii−i−ii-1111-1-1-11-1-111-1111-1-1i−i−iii−i−ii111-1-1-1-11-1-111-11i−i−iii−i−ii
χ71-11-111-1-1-1-11111-1-1-1111-1-1−iii−i−iii−i-1111-1-1-11-1-111-1111-1-1−iii−i−iii−i111-1-1-1-11-1-111-11−iii−i−iii−i
χ81-11-111-1-1-1-11111-1-1-1111-1-1−ii−ii−ii−ii-1111-1-11-111-1-11-111-1-1−ii−ii−ii−ii111-1-1-11-111-1-11-1−ii−ii−ii−ii
χ92222222222222-12-1222-12-100220022222-12-1000000002-12-100220022-1-1-1-1-1-10000000000-1-100-1-1
χ102222222222222-12-1222-12-100-2-200-2-2222-12-1000000002-12-100-2-200-2-2-1-1-1-1-1-10000000000110011
χ11222222222222-12-1222-12-122200220022-12-1200000000-12-1222002200-1-1-1-1-1-100000000-1-100-1-100
χ12222222222222-12-1222-12-12-2-200-2-20022-12-1200000000-12-12-2-200-2-200-1-1-1-1-1-10000000011001100
χ1322-1-12222-1-1-1-1222222-1-1-1-100000000-1-1222222222222-1-1-1-1000000002-1-12-1-1-1-1-1-1-1-1-1-100000000
χ1422-1-12222-1-1-1-1222222-1-1-1-100000000-1-12222-2-2-2-2-2-2-2-2-1-1-1-1000000002-1-12-1-11111111100000000
χ152-22-222-2-2-2-2222-1-21-222-1-21002i−2i002i−2i-222-1-21000000002-1-21002i−2i002i−2i-1-1-11110000000000−ii00−ii
χ162-22-222-2-2-2-2222-1-21-222-1-2100−2i2i00−2i2i-222-1-21000000002-1-2100−2i2i00−2i2i-1-1-11110000000000i−i00i−i
χ172-22-222-2-2-2-222-121-2-22-121-22i−2i002i−2i00-22-121-200000000-121-22i−2i002i−2i00-1-1-111100000000−ii00−ii00
χ182-22-222-2-2-2-222-121-2-22-121-2−2i2i00−2i2i00-22-121-200000000-121-2−2i2i00−2i2i00-1-1-111100000000i−i00i−i00
χ192-2-1122-2-211-1-122-2-2-22-1-111000000001-122-2-22-222-2-22-2-1-111000000002-1-1-211-11-1-111-1100000000
χ202-2-1122-2-211-1-122-2-2-22-1-111000000001-122-2-2-22-2-222-22-1-111000000002-1-1-2111-111-1-11-100000000
χ2133333-13-13-13-10303-1-10303331133-1-1-1-10-10-1111-11-1-1-10-10-1-1-111-1-1-1-1000000111-11-1-1-1001100-1-1
χ2233333-13-13-13-10303-1-1030333-1-13311-1-10-10-1-1-1-11-11110-10-1-1-1-1-1-1-111000000-1-1-11-111100-1-10011
χ2333333-13-13-13-10303-1-10303-3-311-3-3-1-1-1-10-10-1-1-1-11-11110-10-1111111-1-1000000-1-1-11-1111001100-1-1
χ2433333-13-13-13-10303-1-10303-3-3-1-1-3-311-1-10-10-1111-11-1-1-10-10-111-1-11111000000111-11-1-1-100-1-10011
χ253333-13-13-13-133030-1-130301133-1-133-1-1-10-1011-11-11-1-1-10-1011-1-1-1-1-1-100000011-11-11-1-11100-1-100
χ263333-13-13-13-133030-1-1303011-3-3-1-1-3-3-1-1-10-10-1-11-11-111-10-101111-1-111000000-1-11-11-1111100-1-100
χ273333-13-13-13-133030-1-13030-1-1331133-1-1-10-10-1-11-11-111-10-10-1-1-1-111-1-1000000-1-11-11-111-1-1001100
χ283333-13-13-13-133030-1-13030-1-1-3-311-3-3-1-1-10-1011-11-11-1-1-10-10-1-111111100000011-11-11-1-1-1-1001100
χ293-33-33-1-31-313-1030-31-1030-33i−3ii−i3i−3i−ii1-10-1011-11-1-11-110-101−iii−i−ii−ii0000001-11-1-11-1100i−i00−ii
χ303-33-33-1-31-313-1030-31-1030-33i−3i−ii3i−3ii−i1-10-101-11-111-11-10-101−ii−ii−iii−i000000-11-111-11-100−ii00i−i
χ313-33-33-1-31-313-1030-31-1030-3−3i3ii−i−3i3i−ii1-10-101-11-111-11-10-101i−ii−ii−i−ii000000-11-111-11-100i−i00−ii
χ323-33-33-1-31-313-1030-31-1030-3−3i3i−ii−3i3ii−i1-10-1011-11-1-11-110-101i−i−iii−ii−i0000001-11-1-11-1100−ii00i−i
χ333-33-3-131-31-3-1330-301-130-30i−i3i−3i−ii3i−3i1-1-10101-1-111-1-11-1010i−i−ii−ii−ii0000001-1-111-1-11i−i00−ii00
χ343-33-3-131-31-3-1330-301-130-30i−i−3i3i−ii−3i3i1-1-1010-111-1-111-1-1010i−ii−i−iii−i000000-111-1-111-1i−i00−ii00
χ353-33-3-131-31-3-1330-301-130-30−ii3i−3ii−i3i−3i1-1-1010-111-1-111-1-1010−ii−iii−i−ii000000-111-1-111-1−ii00i−i00
χ363-33-3-131-31-3-1330-301-130-30−ii−3i3ii−i−3i3i1-1-10101-1-111-1-11-1010−iii−ii−ii−i0000001-1-111-1-11−ii00i−i00
χ37444444444444-2-2-2-244-2-2-2-20000000044-2-2-2-200000000-2-2-2-2000000001111110000000000000000
χ3844-2-24444-2-2-2-24-24-244-21-2100000000-2-24-24-200000000-21-2100000000-211-2110000000000000000
χ3944-2-24444-2-2-2-2-24-24441-21-200000000-2-2-24-24000000001-21-200000000-211-2110000000000000000
χ4044-2-24444-2-2-2-2-2-2-2-244111100000000-2-2-2-2-2-2000000001111000000001−1−3i32−1+3i321−1−3i32−1+3i320000000000000000
χ4144-2-24444-2-2-2-2-2-2-2-244111100000000-2-2-2-2-2-2000000001111000000001−1+3i32−1−3i321−1+3i32−1−3i320000000000000000
χ424-44-444-4-4-4-444-2-222-44-2-22200000000-44-2-22200000000-2-22200000000111-1-1-10000000000000000
χ434-4-2244-4-422-2-24-2-42-44-212-1000000002-24-2-4200000000-212-100000000-2112-1-10000000000000000
χ444-4-2244-4-422-2-2-242-4-441-2-12000000002-2-242-4000000001-2-1200000000-2112-1-10000000000000000
χ454-4-2244-4-422-2-2-2-222-4411-1-1000000002-2-2-2220000000011-1-1000000001−1−3i32−1+3i32-11+3i321−3i320000000000000000
χ464-4-2244-4-422-2-2-2-222-4411-1-1000000002-2-2-2220000000011-1-1000000001−1+3i32−1−3i32-11−3i321+3i320000000000000000
χ4766666-26-26-26-20-30-3-2-20-30-3002200-2-2-2-20101000000000101002200-2-20000000000000000-1-10011
χ4866666-26-26-26-20-30-3-2-20-30-300-2-20022-2-2010100000000010100-2-2002200000000000000001100-1-1
χ496666-26-26-26-26-30-30-2-2-30-302200-2-200-2-210100000000010102200-2-20000000000000000-1-1001100
χ506666-26-26-26-26-30-30-2-2-30-30-2-2002200-2-21010000000001010-2-2002200000000000000001100-1-100
χ5166-3-36-26-2-31-310606-2-20-30-300000000110-20-2222-22-2-2-2010100000000000000-1-1-11-111100000000
χ5266-3-36-26-2-31-310606-2-20-30-300000000110-20-2-2-2-22-2222010100000000000000111-11-1-1-100000000
χ5366-3-3-26-261-31-36060-2-2-30-300000000011-20-2022-22-22-2-2101000000000000000-1-11-11-11100000000
χ5466-3-3-26-261-31-36060-2-2-30-300000000011-20-20-2-22-22-22210100000000000000011-11-11-1-100000000
χ556-66-66-2-62-626-20-3032-20-303002i−2i00−2i2i2-2010-100000000010-1002i−2i00−2i2i0000000000000000−ii00i−i
χ566-66-66-2-62-626-20-3032-20-30300−2i2i002i−2i2-2010-100000000010-100−2i2i002i−2i0000000000000000i−i00−ii
χ576-66-6-262-62-6-26-30302-2-30302i−2i00−2i2i002-210-100000000010-102i−2i00−2i2i0000000000000000−ii00i−i00
χ586-66-6-262-62-6-26-30302-2-3030−2i2i002i−2i002-210-100000000010-10−2i2i002i−2i0000000000000000i−i00−ii00
χ596-6-336-2-623-1-31060-62-20-30300000000-110-2022-22-2-22-22010-100000000000000-11-111-11-100000000
χ606-6-336-2-623-1-31060-62-20-30300000000-110-202-22-222-22-2010-1000000000000001-11-1-11-1100000000
χ616-6-33-262-6-131-360-602-2-303000000000-11-20202-2-222-2-2210-1000000000000000-111-1-111-100000000
χ626-6-33-262-6-131-360-602-2-303000000000-11-2020-222-2-222-210-10000000000000001-1-111-1-1100000000
χ639999-3-3-3-3-3-3-3-300001100003333-3-3-3-311000011-1-1-1-1110000-1-1-1-1111100000011-1-1-1-11100000000
χ649999-3-3-3-3-3-3-3-3000011000033-3-3-3-333110000-1-11111-1-10000-1-11111-1-1000000-1-11111-1-100000000
χ659999-3-3-3-3-3-3-3-30000110000-3-33333-3-3110000-1-11111-1-1000011-1-1-1-111000000-1-11111-1-100000000
χ669999-3-3-3-3-3-3-3-30000110000-3-3-3-3333311000011-1-1-1-11100001111-1-1-1-100000011-1-1-1-11100000000
χ679-99-9-3-33333-3-30000-1100003i−3i3i−3i−3i3i−3i3i-1100001-1-1-1111-10000−ii−iii−ii−i0000001-1-1-1111-100000000
χ689-99-9-3-33333-3-30000-1100003i−3i−3i3i−3i3i3i−3i-110000-1111-1-1-110000−iii−ii−i−ii000000-1111-1-1-1100000000
χ699-99-9-3-33333-3-30000-110000−3i3i3i−3i3i−3i−3i3i-110000-1111-1-1-110000i−i−ii−iii−i000000-1111-1-1-1100000000
χ709-99-9-3-33333-3-30000-110000−3i3i−3i3i3i−3i3i−3i-1100001-1-1-1111-10000i−ii−i−ii−ii0000001-1-1-1111-100000000
χ711212-6-612-412-4-62-620-60-6-4-4030300000000220202000000000-10-1000000000000000000000000000000
χ721212-6-6-412-4122-62-6-60-60-4-430300000000022202000000000-10-10000000000000000000000000000000
χ7312-12-6612-4-1246-2-620-6064-4030-300000000-22020-2000000000-101000000000000000000000000000000
χ7412-12-66-4124-12-262-6-60604-430-3000000000-2220-2000000000-1010000000000000000000000000000000
χ751818-9-9-6-6-6-63333000022000000000000-1-1000022-2-2-2-222000000000000000000-1-11111-1-100000000
χ761818-9-9-6-6-6-63333000022000000000000-1-10000-2-22222-2-200000000000000000011-1-1-1-11100000000
χ7718-18-99-6-666-3-3330000-220000000000001-100002-2-2-2222-2000000000000000000-1111-1-1-1100000000
χ7818-18-99-6-666-3-3330000-220000000000001-10000-2222-2-2-220000000000000000001-1-1-1111-100000000

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