Finite Group Databasebeta

← Group #72230976

Character table — Group #72230976

Order 4800.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122244444488888888888888888881616161616161616161616161616161616161616161616161616252550505060606060100100100100100100100100100100120120120120150150150150200200200240240300300
order1234625510101255610101515151515152020303030303030101010101010202030303030303030303030303060606060606022466448824488122424242440404040444461212202044
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-11-1-111-1-1
χ31111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-1-11-11-1-1i−ii−i-1ii−i−i11-1-1i−ii−i-1i−i1-1i−i
χ611111111111111111111111111111111111111111111111111111111-1-1-1-1-11-11-1-1−ii−ii-1−i−iii11-1-1−ii−ii-1−ii1-1−ii
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11-11-1i−ii−i-1ii−i−i-1-111−ii−ii-1i−i-11−ii
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11-11-1−ii−ii-1−i−iii-1-111i−ii−i-1−ii-11i−i
χ911111-11111111-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-111-1-11-1-1-1-1-1-1-1-11111-11111-1-1
χ1011111-11111111-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-11111
χ1111111-11111111-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-111-1-11-1-1-1-11111-1-1-1-1-111-1-111
χ1211111-11111111-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1-1-1111111111111111-1-1-1-1-1-1-1
χ1311111-11111111-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-111i−i−ii-1−i−iii-1-111i−ii−i1i−i1-1−ii
χ1411111-11111111-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-111−iii−i-1ii−i−i-1-111−ii−ii1−ii1-1i−i
χ1511111-11111111-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-11i−i−ii-1−i−iii11-1-1−ii−ii1i−i-11i−i
χ1611111-11111111-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-11−iii−i-1ii−i−i11-1-1i−ii−i1−ii-11−ii
χ17222-2202222-222022222222-2-2222222000000-2-2000000000000-2-2-2-2-2-222-222000000000-20000000022-2-20000000
χ18222-2202222-222022222222-2-2222222000000-2-2000000000000-2-2-2-2-2-222-222000000000-200000000-2-2220000000
χ19222-2202222-222022222222-2-2222222000000-2-2000000000000-2-2-2-2-2-2-2-22-2-20000000002000000002i−2i−2i2i0000000
χ20222-2202222-222022222222-2-2222222000000-2-2000000000000-2-2-2-2-2-2-2-22-2-2000000000200000000−2i2i2i−2i0000000
χ2122-12-122222-122-122-1-1-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1000022222-1-1-1-1-100000000-1-1-10000
χ2222-12-122222-122-122-1-1-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-100002-2-2-2-2-1111100000000-1110000
χ2322-12-122222-122-122-1-1-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2110000-22i−2i2i−2i1−i−iii000000001−ii0000
χ2422-12-122222-122-122-1-1-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2110000-2−2i2i−2i2i1ii−i−i000000001i−i0000
χ2522-12-1-22222-122122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-222111111111111-1-1-1-1-1-1222-1-10000-222-2-2-11111000000001-1-10000
χ2622-12-1-22222-122122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-222111111111111-1-1-1-1-1-1222-1-10000-2-2-222-1-1-1-1-1000000001110000
χ2722-12-1-22222-122122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-222111111111111-1-1-1-1-1-1-2-2-211000022i−2i−2i2i1ii−i−i00000000-1−ii0000
χ2822-12-1-22222-122122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-222111111111111-1-1-1-1-1-1-2-2-21100002−2i2i2i−2i1−i−iii00000000-1i−i0000
χ294444444-14-14-1-14-1-14-1-1-1-1-14-14-1-1-1-1-14-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-14-1-1-1-1-1000000404000000000000-1-100000000-100
χ304444444-14-14-1-14-1-14-1-1-1-1-14-14-1-1-1-1-14-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-14-1-1-1-1-1000000-40-40000000000001100000000100
χ31444444-14-144-1-14-1-1-14-1-1-1-1-14-14-1-1-1-1-14-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-14-1-1-1-10000040400000000000-1-1000000000-1000
χ32444444-14-144-1-14-1-1-14-1-1-1-1-14-14-1-1-1-1-14-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-14-1-1-1-100000-40-400000000000110000000001000
χ3344444-44-14-14-1-1-4-1-14-1-1-1-1-14-14-1-1-1-1-1-411111-1-1-4-411111111114-1-1-1-1-100000040-40000000000001100000000-100
χ3444444-44-14-14-1-1-4-1-14-1-1-1-1-14-14-1-1-1-1-1-411111-1-1-4-411111111114-1-1-1-1-1000000-404000000000000-1-100000000100
χ3544444-4-14-144-1-1-4-1-1-14-1-1-1-1-14-14-1-1-1-11-41111-1-111-4-411111111-14-1-1-1-10000040-40000000000011000000000-1000
χ3644444-4-14-144-1-1-4-1-1-14-1-1-1-1-14-14-1-1-1-11-41111-1-111-4-411111111-14-1-1-1-100000-40400000000000-1-10000000001000
χ3744-2-4-204444244044-2-2-2-2-2-2-4-4-2-2-2-2-2-2000000-4-400000000000022222244-4-2-200000000020000000000000000000
χ3844-2-4-204444244044-2-2-2-2-2-2-4-4-2-2-2-2-2-2000000-4-4000000000000222222-4-4422000000000-20000000000000000000
χ394-440-4044-4-40440-4-444444400-4-4-4-4-4-4000000000000000000000000004-404-400000000000000000000000000000
χ404-440-4044-4-40440-4-444444400-4-4-4-4-4-400000000000000000000000000-440-4400000000000000000000000000000
χ414-4-202044-4-40440-4-4-2-2-2-2-2-200222222000000000000000000000000004-40-2200000000006−66−6000000000000000
χ424-4-202044-4-40440-4-4-2-2-2-2-2-200222222000000000000000000000000004-40-220000000000−66−66000000000000000
χ434-4-202044-4-40440-4-4-2-2-2-2-2-20022222200000000000000000000000000-4402-20000000000−i6i6i6−i6000000000000000
χ444-4-202044-4-40440-4-4-2-2-2-2-2-20022222200000000000000000000000000-4402-20000000000i6−i6−i6i6000000000000000
χ45888888-2-2-2-283-283-2-2-233-2-2-2-2-2-233-2-2-2-233-2-23-2-2-2-2-23333-2-2-2-2-2-233-2-20000000000000000000000000000000000
χ46888888-2-2-2-28-238-23-2-2-2-233-2-2-2-2-2-233-2-2-2-233-23-2-2-2-2-2-2-2-23333-2-2-2-2330000000000000000000000000000000000
χ4788888-8-2-2-2-283-2-83-2-2-233-2-2-2-2-2-233-2-222-3-3223-22222-3-3-3-32222-2-233-2-20000000000000000000000000000000000
χ4888888-8-2-2-2-28-23-8-23-2-2-2-233-2-2-2-2-2-2332222-3-3-2322222222-3-3-3-3-2-2-2-2330000000000000000000000000000000000
χ49888-8808-28-2-8-2-20-2-28-2-2-2-2-2-828-2-2-2-2-200000022000000000000-8222220000000000000000000000000000000000
χ50888-880-28-28-8-2-20-2-2-28-2-2-2-22-8-28-2-2-2-2000000220000000000002-822220000000000000000000000000000000000
χ51888-880-2-2-2-2-83-203-2-2-233-2-222-2-233-2-2005-500-32000055-5-5000022-3-3220000000000000000000000000000000000
χ52888-880-2-2-2-2-83-203-2-2-233-2-222-2-233-2-200-5500-320000-5-555000022-3-3220000000000000000000000000000000000
χ53888-880-2-2-2-2-8-230-23-2-2-2-23322-2-2-2-23300005-52-30000000055-5-52222-3-30000000000000000000000000000000000
χ54888-880-2-2-2-2-8-230-23-2-2-2-23322-2-2-2-2330000-552-300000000-5-5552222-3-30000000000000000000000000000000000
χ5588-48-488-28-2-4-2-2-4-2-2-4111118-2-4111118-2-2-2-2-2-2-2-4-41111111111-4111110000000000000000000000000000000000
χ5688-48-48-28-28-4-2-2-4-2-21-41111-281-41111-28-2-2-2-2-2-211-4-4111111111-411110000000000000000000000000000000000
χ5788-48-48-2-2-2-2-43-2-43-211−3−i152−3+i1521−i151+i15-2-211−3−i152−3+i1521−i151+i15-2-233-2-23-21111−3−i152−3+i152−3−i152−3+i1521−i151+i151−i151+i1511−3−i152−3+i1521−i151+i150000000000000000000000000000000000
χ5888-48-48-2-2-2-2-43-2-43-211−3+i152−3−i1521+i151−i15-2-211−3+i152−3−i1521+i151−i15-2-233-2-23-21111−3+i152−3−i152−3+i152−3−i1521+i151−i151+i151−i1511−3+i152−3−i1521+i151−i150000000000000000000000000000000000
χ5988-48-48-2-2-2-2-4-23-4-23111−i151+i15−3+i152−3−i152-2-2111−i151+i15−3+i152−3−i152-2-2-2-233-2311111−i151+i151−i151+i15−3+i152−3−i152−3+i152−3−i152111−i151+i15−3+i152−3−i1520000000000000000000000000000000000
χ6088-48-48-2-2-2-2-4-23-4-23111+i151−i15−3−i152−3+i152-2-2111+i151−i15−3−i152−3+i152-2-2-2-233-2311111+i151−i151+i151−i15−3−i152−3+i152−3−i152−3+i152111+i151−i15−3−i152−3+i1520000000000000000000000000000000000
χ6188-48-4-88-28-2-4-2-24-2-2-4111118-2-411111-822222-2-244-1-1-1-1-1-1-1-1-1-1-4111110000000000000000000000000000000000
χ6288-48-4-8-28-28-4-2-24-2-21-41111-281-411112-82222-2-2-1-144-1-1-1-1-1-1-1-11-411110000000000000000000000000000000000
χ6388-48-4-8-2-2-2-2-43-243-211−3−i152−3+i1521−i151+i15-2-211−3−i152−3+i1521−i151+i1522-3-3223-2-1-1-1-13+i1523−i1523+i1523−i152−1+i15−1−i15−1+i15−1−i1511−3−i152−3+i1521−i151+i150000000000000000000000000000000000
χ6488-48-4-8-2-2-2-2-43-243-211−3+i152−3−i1521+i151−i15-2-211−3+i152−3−i1521+i151−i1522-3-3223-2-1-1-1-13−i1523+i1523−i1523+i152−1−i15−1+i15−1−i15−1+i1511−3+i152−3−i1521+i151−i150000000000000000000000000000000000
χ6588-48-4-8-2-2-2-2-4-234-23111−i151+i15−3+i152−3−i152-2-2111−i151+i15−3+i152−3−i1522222-3-3-23-1-1-1-1−1+i15−1−i15−1+i15−1−i153−i1523+i1523−i1523+i152111−i151+i15−3+i152−3−i1520000000000000000000000000000000000
χ6688-48-4-8-2-2-2-2-4-234-23111+i151−i15−3−i152−3+i152-2-2111+i151−i15−3−i152−3+i1522222-3-3-23-1-1-1-1−1−i15−1+i15−1−i15−1+i153+i1523−i1523+i1523−i152111+i151−i15−3−i152−3+i1520000000000000000000000000000000000
χ6788-4-8-408-28-24-2-20-2-2-411111-82-4111110000002200−i15i15−i15i15i15−i15−i15i15i15−i154-1-1-1-1-10000000000000000000000000000000000
χ6888-4-8-408-28-24-2-20-2-2-411111-82-4111110000002200i15−i15i15−i15−i15i15i15−i15−i15i154-1-1-1-1-10000000000000000000000000000000000
χ6988-4-8-40-28-284-2-20-2-21-411112-81-4111100000022−i15i1500−i15i15i15−i15i15−i15−i15i15-14-1-1-1-10000000000000000000000000000000000
χ7088-4-8-40-28-284-2-20-2-21-411112-81-4111100000022i15−i1500i15−i15−i15i15−i15i15i15−i15-14-1-1-1-10000000000000000000000000000000000
χ7188-4-8-40-2-2-2-243-203-211−3−i152−3+i1521−i151+i152211−3−i152−3+i1521−i151+i15005-500-32−i15i15−i15i15−5+i152−5−i1525−i1525+i1520000-1-13+i1523−i152−1+i15−1−i150000000000000000000000000000000000
χ7288-4-8-40-2-2-2-243-203-211−3−i152−3+i1521−i151+i152211−3−i152−3+i1521−i151+i1500-5500-32i15−i15i15−i155−i1525+i152−5+i152−5−i1520000-1-13+i1523−i152−1+i15−1−i150000000000000000000000000000000000
χ7388-4-8-40-2-2-2-243-203-211−3+i152−3−i1521+i151−i152211−3+i152−3−i1521+i151−i15005-500-32i15−i15i15−i15−5−i152−5+i1525+i1525−i1520000-1-13−i1523+i152−1−i15−1+i150000000000000000000000000000000000
χ7488-4-8-40-2-2-2-243-203-211−3+i152−3−i1521+i151−i152211−3+i152−3−i1521+i151−i1500-5500-32−i15i15−i15i155+i1525−i152−5−i152−5+i1520000-1-13−i1523+i152−1−i15−1+i150000000000000000000000000000000000
χ7588-4-8-40-2-2-2-24-230-23111−i151+i15−3+i152−3−i15222111−i151+i15−3+i152−3−i15200005-52-3−i15i15i15−i150000−5−i152−5+i1525+i1525−i152-1-1−1+i15−1−i153−i1523+i1520000000000000000000000000000000000
χ7688-4-8-40-2-2-2-24-230-23111−i151+i15−3+i152−3−i15222111−i151+i15−3+i152−3−i1520000-552-3i15−i15−i15i1500005+i1525−i152−5−i152−5+i152-1-1−1+i15−1−i153−i1523+i1520000000000000000000000000000000000
χ7788-4-8-40-2-2-2-24-230-23111+i151−i15−3−i152−3+i15222111+i151−i15−3−i152−3+i15200005-52-3i15−i15−i15i150000−5+i152−5−i1525−i1525+i152-1-1−1−i15−1+i153+i1523−i1520000000000000000000000000000000000
χ7888-4-8-40-2-2-2-24-230-23111+i151−i15−3−i152−3+i15222111+i151−i15−3−i152−3+i1520000-552-3−i15i15i15−i1500005−i1525+i152−5+i152−5−i152-1-1−1−i15−1+i153+i1523−i1520000000000000000000000000000000000
χ798-880-808-2-820-2-20228-2-2-2-2-200-82222200000000000000000000000000000000000000000000000i10−i1000000000000
χ808-880-808-2-820-2-20228-2-2-2-2-200-82222200000000000000000000000000000000000000000000000−i10i1000000000000
χ818-880-80-282-80-2-2022-28-2-2-2-2002-82222000000000000000000000000000000000000000000000i10−i100000000000000
χ828-880-80-282-80-2-2022-28-2-2-2-2002-82222000000000000000000000000000000000000000000000−i10i100000000000000
χ8316-16160-160-4-44406-40-64-4-466-4-40044-6-644000000000000000000000000000000000000000000000000000000000000
χ8416-16160-160-4-4440-4604-6-4-4-4-466004444-6-6000000000000000000000000000000000000000000000000000000000000
χ8516-16-808016-4-1640-4-4044-822222008-2-2-2-2-2000000000000000000000000000000000000000000000000000000000000
χ8616-16-8080-4164-160-4-40442-8222200-28-2-2-2-2000000000000000000000000000000000000000000000000000000000000
χ8716-16-8080-4-44406-40-6422−3−i15−3+i152−2i152+2i1500-2-23+i153−i15−2+2i15−2−2i15000000000000000000000000000000000000000000000000000000000000
χ8816-16-8080-4-44406-40-6422−3+i15−3−i152+2i152−2i1500-2-23−i153+i15−2−2i15−2+2i15000000000000000000000000000000000000000000000000000000000000
χ8916-16-8080-4-4440-4604-6222−2i152+2i15−3+i15−3−i1500-2-2−2+2i15−2−2i153−i153+i15000000000000000000000000000000000000000000000000000000000000
χ9016-16-8080-4-4440-4604-6222+2i152−2i15−3−i15−3+i1500-2-2−2−2i15−2+2i153+i153−i15000000000000000000000000000000000000000000000000000000000000

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