Finite Group Databasebeta

← Group #72269081

Character table — Group #72269081

Order 5184.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11244448888889999161616161616161616161616161616161818363636367272727272728181108108108108108108108108162162162162162162162162162216216216216216216216216
order122336636666644443333666666666666441212121212121212121222888888882444444442424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ51111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−iii−i−i11111-1-1-1-1ii−i−iii−i−i
χ61111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii1-1-1-1-11111ii−i−i−i−iii
χ71111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i1-1-1-1-11111−i−iiiii−i−i
χ81111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111−i−iii−i−iii11111-1-1-1-1−i−iii−i−iii
χ911-111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111-11-11-11-1-111-1-111-1-11-11-11-11-1
χ1011-111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111-11-1-11-11-1-1-111-1-1111-11-1-11-11
χ1111-111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11-111-11-1-1-1-111-1-111-11-111-11-1
χ1211-111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11-11-11-11-111-1-111-1-1-11-11-11-11
χ1311-111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111i−i−iii−i−ii-111-1-1-1-111i−i−iii−i−ii
χ1411-111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111i−i−ii−iii−i-1-1-11111-1-1i−i−ii−iii−i
χ1511-111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111−iii−ii−i−ii-1-1-11111-1-1−iii−ii−i−ii
χ1611-111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111−iii−i−iii−i-111-1-1-1-111−iii−i−iii−i
χ17222222222222222-2-222222222222222222-2-2-2-2-2-2-22222-2-200000000-20000000000000000
χ182222222222222-2-2222222222222222222-22222222-2-2-2-2-2-200000000-20000000000000000
χ1922-222222-2-2-2-2222-2-222222222-2-2-2-2-2-2-2-2-22-2-2-2-22222-2-2-2-20000000020000000000000000
χ2022-222222-2-2-2-22-2-22222222222-2-2-2-2-2-2-2-22-22222-2-2-2-222-2-20000000020000000000000000
χ212-2022-2-220000-22i−2i2i−2i2222-2-2-2-200000000002i2i−2i−2i002i−2i002-2000000000002i−2i002-200000000
χ222-2022-2-220000-22i−2i2i−2i2222-2-2-2-200000000002i2i−2i−2i002i−2i002-200000000000−2i2i00-2200000000
χ232-2022-2-220000-22i−2i−2i2i2222-2-2-2-20000000000−2i−2i2i2i002i−2i00-220000000002-2002i−2i0000000000
χ242-2022-2-220000-22i−2i−2i2i2222-2-2-2-20000000000−2i−2i2i2i002i−2i00-22000000000-2200−2i2i0000000000
χ252-2022-2-220000-2−2i2i2i−2i2222-2-2-2-200000000002i2i−2i−2i00−2i2i00-220000000002-200−2i2i0000000000
χ262-2022-2-220000-2−2i2i2i−2i2222-2-2-2-200000000002i2i−2i−2i00−2i2i00-22000000000-22002i−2i0000000000
χ272-2022-2-220000-2−2i2i−2i2i2222-2-2-2-20000000000−2i−2i2i2i00−2i2i002-2000000000002i−2i00-2200000000
χ282-2022-2-220000-2−2i2i−2i2i2222-2-2-2-20000000000−2i−2i2i2i00−2i2i002-200000000000−2i2i002-200000000
χ294441-21-241-2444004411-2-211-2-21111-2-2-2-2041-21-21-2000000000022220000000000000-1-1-1-1
χ304441-21-241-2444004411-2-211-2-21111-2-2-2-2041-21-21-20000000000-2-2-2-200000000000001111
χ314441-21-241-244400-4-411-2-211-2-21111-2-2-2-20-4-12-12-1200000000002i2i−2i−2i0000000000000−i−iii
χ324441-21-241-244400-4-411-2-211-2-21111-2-2-2-20-4-12-12-120000000000−2i−2i2i2i0000000000000ii−i−i
χ33444-21-214-214440044-2-211-2-211-2-2-2-2111104-21-21-2100000022220000000000000-1-1-1-10000
χ34444-21-214-214440044-2-211-2-211-2-2-2-2111104-21-21-21000000-2-2-2-2000000000000011110000
χ35444-21-214-2144400-4-4-2-211-2-211-2-2-2-211110-42-12-12-10000002i2i−2i−2i0000000000000−i−iii0000
χ36444-21-214-2144400-4-4-2-211-2-211-2-2-2-211110-42-12-12-1000000−2i−2i2i2i0000000000000ii−i−i0000
χ3744-41-21-24-12-4-44004411-2-211-2-2-1-1-1-122220-41-21-2-1200000000002-22-20000000000000-11-11
χ3844-41-21-24-12-4-44004411-2-211-2-2-1-1-1-122220-41-21-2-120000000000-22-2200000000000001-11-1
χ3944-41-21-24-12-4-4400-4-411-2-211-2-2-1-1-1-1222204-12-121-200000000002i−2i−2i2i0000000000000−iii−i
χ4044-41-21-24-12-4-4400-4-411-2-211-2-2-1-1-1-1222204-12-121-20000000000−2i2i2i−2i0000000000000i−i−ii
χ4144-4-21-2142-1-4-440044-2-211-2-2112222-1-1-1-10-4-21-212-10000002-22-20000000000000-11-110000
χ4244-4-21-2142-1-4-440044-2-211-2-2112222-1-1-1-10-4-21-212-1000000-22-2200000000000001-11-10000
χ4344-4-21-2142-1-4-4400-4-4-2-211-2-2112222-1-1-1-1042-12-1-210000002i−2i−2i2i0000000000000−iii−i0000
χ4444-4-21-2142-1-4-4400-4-4-2-211-2-2112222-1-1-1-1042-12-1-21000000−2i2i2i−2i0000000000000i−i−ii0000
χ458888888-188-1-1-18800-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-180000000-1-1-1-1000000000000000000000000000
χ468888888-188-1-1-1-8-800-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-800000001111000000000000000000000000000
χ4788-88888-1-8-811-18800-1-1-1-1-1-1-1-111111111-80000000-1-111000000000000000000000000000
χ4888-88888-1-8-811-1-8-800-1-1-1-1-1-1-1-1111111118000000011-1-1000000000000000000000000000
χ498-802-4-2480000-8008i−8i22-4-4-2-24400000000002i−4i−2i4i000000000000000000000000000000000
χ508-802-4-2480000-800−8i8i22-4-4-2-2440000000000−2i4i2i−4i000000000000000000000000000000000
χ518-8088-8-8-1003-318i−8i00-1-1-1-1111133-3-333-3-300000000−ii3i−3i000000000000000000000000000
χ528-8088-8-8-1003-31−8i8i00-1-1-1-1111133-3-333-3-300000000i−i−3i3i000000000000000000000000000
χ538-8088-8-8-100-3318i−8i00-1-1-1-11111-3-333-3-33300000000−ii−3i3i000000000000000000000000000
χ548-8088-8-8-100-331−8i8i00-1-1-1-11111-3-333-3-33300000000i−i3i−3i000000000000000000000000000
χ558-80-424-280000-8008i−8i-4-42244-2-20000000000−4i2i4i−2i000000000000000000000000000000000
χ568-80-424-280000-800−8i8i-4-42244-2-200000000004i−2i−4i2i000000000000000000000000000000000
χ571616164-84-8-24-8-2-2-200004-5114-5114-54-51111000000000000000000000000000000000000000
χ581616164-84-8-24-8-2-2-20000-5411-5411-54-541111000000000000000000000000000000000000000
χ59161616-84-84-2-84-2-2-20000114-5114-511114-54-5000000000000000000000000000000000000000
χ60161616-84-84-2-84-2-2-2000011-5411-541111-54-54000000000000000000000000000000000000000
χ611616-164-84-8-2-4822-200004-5114-511-45-45-1-1-1-1000000000000000000000000000000000000000
χ621616-164-84-8-2-4822-20000-5411-54115-45-4-1-1-1-1000000000000000000000000000000000000000
χ631616-16-84-84-28-422-20000114-5114-5-1-1-1-1-45-45000000000000000000000000000000000000000
χ641616-16-84-84-28-422-2000011-5411-54-1-1-1-15-45-4000000000000000000000000000000000000000
χ6516-1604-8-48-2006-6200004-511-45-1-16-3-63-3-333000000000000000000000000000000000000000
χ6616-1604-8-48-2006-620000-54115-4-1-1-363-6-3-333000000000000000000000000000000000000000
χ6716-1604-8-48-200-66200004-511-45-1-1-636-333-3-3000000000000000000000000000000000000000
χ6816-1604-8-48-200-6620000-54115-4-1-13-6-3633-3-3000000000000000000000000000000000000000
χ6916-160-848-4-2006-620000114-5-1-1-45-3-3336-3-63000000000000000000000000000000000000000
χ7016-160-848-4-2006-62000011-54-1-15-4-3-333-363-6000000000000000000000000000000000000000
χ7116-160-848-4-200-6620000114-5-1-1-4533-3-3-636-3000000000000000000000000000000000000000
χ7216-160-848-4-200-662000011-54-1-15-433-3-33-6-36000000000000000000000000000000000000000

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