Finite Group Databasebeta

← Group #72260306

Character table — Group #72260306

Order 4800.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11334444888888121212122424242425253232323232323232323232325050606060607575120120120120120120120120150150200200200200200200300300300300
order1222551010355610101010101010101010221515151515153030303030304422442210101010202020204466121212124444
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ3111111111111111111111111111111111111-1-111111111111111-1-111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111111111111111-1-1111111111111i−i1-11-1-1-111-1-111-1-1i−i-1-1ii−i−ii−ii−i
χ61111111111111111111111-1-1111111111111i−i-11-11-1-1-1-111-1-111i−i-1-1ii−i−i−ii−ii
χ71111111111111111111111-1-1111111111111−ii1-11-1-1-111-1-111-1-1−ii-1-1−i−iii−ii−ii
χ81111111111111111111111-1-1111111111111−ii-11-11-1-1-1-111-1-111−ii-1-1−i−iiii−ii−i
χ922222222-122-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1220000220000000022-1-1-1-1-1-10000
χ1022222222-122-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-2-200002200000000-2-2-1-111110000
χ1122222222-122-12222222222-2-2-1-1-1-1-1-1-1-1-1-1-1-12i−2i0000-2-2000000002i−2i11−i−iii0000
χ1222222222-122-12222222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1−2i2i0000-2-200000000−2i2i11ii−i−i0000
χ132-2-2222-2-2222-2-2-2-2-22222-2-22-2222222-2-2-2-2-2-20000002-20000000000-2200000000
χ142-2-2222-2-2222-2-2-2-2-22222-2-2-22222222-2-2-2-2-2-2000000-2200000000002-200000000
χ152-2-2222-2-2-1221-2-2-2-22222-2-22-2-1-1-1-1-1-11111110000002-200000000001-1−i3i3−i3i30000
χ162-2-2222-2-2-1221-2-2-2-22222-2-22-2-1-1-1-1-1-11111110000002-200000000001-1i3−i3i3−i30000
χ172-2-2222-2-2-1221-2-2-2-22222-2-2-22-1-1-1-1-1-1111111000000-220000000000-113−3−330000
χ182-2-2222-2-2-1221-2-2-2-22222-2-2-22-1-1-1-1-1-1111111000000-220000000000-11−333−30000
χ1933-1-13333033033-1-1-1-1-1-1-1-1330000000000003311-1-1-1-11111-1-1-1-1-1-100000011-1-1
χ2033-1-13333033033-1-1-1-1-1-1-1-13300000000000033-1-111-1-1-1-1-1-11111-1-1000000-1-111
χ2133-1-13333033033-1-1-1-1-1-1-1-133000000000000-3-311-1-1-1-11111-1-1-1-111000000-1-111
χ2233-1-13333033033-1-1-1-1-1-1-1-133000000000000-3-3-1-111-1-1-1-1-1-111111100000011-1-1
χ2333-1-13333033033-1-1-1-1-1-1-1-1-3-30000000000003i−3i1-1-111111-1-1-1-111−ii000000i−i−ii
χ2433-1-13333033033-1-1-1-1-1-1-1-1-3-30000000000003i−3i-111-111-1-11111-1-1−ii000000−iii−i
χ2533-1-13333033033-1-1-1-1-1-1-1-1-3-3000000000000−3i3i1-1-111111-1-1-1-111i−i000000−iii−i
χ2633-1-13333033033-1-1-1-1-1-1-1-1-3-3000000000000−3i3i-111-111-1-11111-1-1i−i000000i−i−ii
χ2744444-14-14-1-14-1-14-14-1-1-1-1-1004-1-1-1-1-14-1-1-1-1-10004040000-1-100-1-1000000000000
χ2844444-14-14-1-14-1-14-14-1-1-1-1-1004-1-1-1-1-14-1-1-1-1-1000-40-40000110011000000000000
χ294444-14-144-1-14-1-1-14-14-1-1-1-100-14-1-1-1-1-14-1-1-1-100404000-1-100-1-100000000000000
χ304444-14-144-1-14-1-1-14-14-1-1-1-100-14-1-1-1-1-14-1-1-1-100-40-400011001100000000000000
χ314-4-444-1-414-1-1-411-414-1-1-111004-1-1-1-1-1-4111110000000000−5500−55000000000000
χ324-4-444-1-414-1-1-411-414-1-1-111004-1-1-1-1-1-41111100000000005−5005−5000000000000
χ334-4-44-141-44-1-1-4111-4-14-1-11100-14-1-1-1-11-4111100000000−5500−5500000000000000
χ344-4-44-141-44-1-1-4111-4-14-1-11100-14-1-1-1-11-41111000000005−5005−500000000000000
χ356-62-266-6-60660-6-622-2-2-2-2226-6000000000000000000-2200000000000000000000
χ366-62-266-6-60660-6-622-2-2-2-222-660000000000000000002-200000000000000000000
χ3788888-28-2-4-2-2-4-2-28-28-2-2-2-2-200-411111-4111110000000000000000000000000000
χ388888-28-28-4-2-2-4-2-2-28-28-2-2-2-2001-411111-411110000000000000000000000000000
χ398888-2-2-2-283-283-2-2-2-2-23-23-200-2-233-2-2-2-233-2-20000000000000000000000000000
χ408888-2-2-2-28-238-23-2-2-2-2-23-2300-2-2-2-233-2-2-2-2330000000000000000000000000000
χ418888-2-2-2-2-43-2-43-2-2-2-2-23-23-20011−3−i152−3+i1521−i151+i1511−3−i152−3+i1521−i151+i150000000000000000000000000000
χ428888-2-2-2-2-43-2-43-2-2-2-2-23-23-20011−3+i152−3−i1521+i151−i1511−3+i152−3−i1521+i151−i150000000000000000000000000000
χ438888-2-2-2-2-4-23-4-23-2-2-2-2-23-2300111−i151+i15−3+i152−3−i152111−i151+i15−3+i152−3−i1520000000000000000000000000000
χ448888-2-2-2-2-4-23-4-23-2-2-2-2-23-2300111+i151−i15−3−i152−3+i152111+i151−i15−3−i152−3+i1520000000000000000000000000000
χ458-8-888-2-82-4-2-2422-828-2-2-22200-4111114-1-1-1-1-10000000000000000000000000000
χ468-8-88-282-8-4-2-24222-8-28-2-222001-41111-14-1-1-1-10000000000000000000000000000
χ478-8-88-2-22283-2-8-3222-2-23-2-3200-2-233-2-222-3-3220000000000000000000000000000
χ488-8-88-2-2228-23-82-322-2-2-232-300-2-2-2-2332222-3-30000000000000000000000000000
χ498-8-88-2-222-43-24-3222-2-23-2-320011−3−i152−3+i1521−i151+i15-1-13+i1523−i152−1+i15−1−i150000000000000000000000000000
χ508-8-88-2-222-43-24-3222-2-23-2-320011−3+i152−3−i1521+i151−i15-1-13−i1523+i152−1−i15−1+i150000000000000000000000000000
χ518-8-88-2-222-4-2342-322-2-2-232-300111−i151+i15−3+i152−3−i152-1-1−1+i15−1−i153−i1523+i1520000000000000000000000000000
χ528-8-88-2-222-4-2342-322-2-2-232-300111+i151−i15−3−i152−3+i152-1-1−1−i15−1+i153+i1523−i1520000000000000000000000000000
χ531212-4-412-312-30-3-30-3-3-41-4111110000000000000000040-40000-1-10011000000000000
χ541212-4-412-312-30-3-30-3-3-41-41111100000000000000000-40400001100-1-1000000000000
χ551212-4-4-312-3120-3-30-3-31-41-41111000000000000000040-4000-1-1001100000000000000
χ561212-4-4-312-3120-3-30-3-31-41-411110000000000000000-4040001100-1-100000000000000
χ5712-124-412-3-1230-3-30334-1-4111-1-1000000000000000000000000−55005−5000000000000
χ5812-124-412-3-1230-3-30334-1-4111-1-10000000000000000000000005−500−55000000000000
χ5912-124-4-3123-120-3-3033-141-411-1-10000000000000000000000−55005−500000000000000
χ6012-124-4-3123-120-3-3033-141-411-1-100000000000000000000005−500−5500000000000000
χ612424-8-8-6-6-6-609-609-62222-32-32000000000000000000000000000000000000000000
χ622424-8-8-6-6-6-60-690-6922222-32-3000000000000000000000000000000000000000000
χ6324-248-8-6-66609-60-96-2-222-323-2000000000000000000000000000000000000000000
χ6424-248-8-6-6660-6906-9-2-2222-3-23000000000000000000000000000000000000000000

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