Finite Group Databasebeta

← Group #10592551

Character table — Group #10592551

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222222222222244444444444444444444444444448888888888888888999918181818181836363636
order1222333344666666666666888844441212121212121212242424242424242424242424242424241212121212121212121212121212121244444488882244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1
χ91-1-1111111-11111-1-1-1-1-1-1-1-111-1-1i−ii−i-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−ii−iii−i−i1-11-1
χ101-1-1111111-11111-1-1-1-1-1-1-1-111-1-1i−ii−i-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−ii−i−iii-11-11
χ111-1-1111111-11111-1-1-1-1-1-1-1-111-1-1−ii−ii-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−ii−iii−i−i-11-11
χ121-1-1111111-11111-1-1-1-1-1-1-1-111-1-1−ii−ii-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−ii−i−iii1-11-1
χ131-1-1111111-11111-1-1-1-1-1-1-1-1-1-111i−i−ii-1-1-1-11111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiiii−i−ii−i−i−iii1-1-11
χ141-1-1111111-11111-1-1-1-1-1-1-1-1-1-111i−i−ii-1-1-1-11111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−i−iii−iiii−i−i-111-1
χ151-1-1111111-11111-1-1-1-1-1-1-1-1-1-111−iii−i-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−iii−i−ii−i−i−iii-111-1
χ161-1-1111111-11111-1-1-1-1-1-1-1-1-1-111−iii−i-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−i−iii−iiii−i−i1-1-11
χ1722222222-2-222222222222200000000-2-2-2-2-2-2-2-2000000000000000000000000000000002222-2-200000000
χ1822222222-2-222222222222200000000-2-2-2-2-2-2-2-200000000000000000000000000000000-2-2-2-22200000000
χ1922222-1-1-1222-1-1-122-1-1-1-1-1-1222222222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-100000000000000
χ2022222-1-1-1222-1-1-122-1-1-1-1-1-12222-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2111-2111-2111-211100000000000000
χ2122222-1-1-1222-1-1-122-1-1-1-1-1-1-2-2-2-222-2-22-1-1-12-1-1-1-2-2111111-2-21111112-1-1-12-1-1-1-2111-211100000000000000
χ2222222-1-1-1222-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2222-1-1-12-1-1-1-2-2111111-2-2111111-2111-21112-1-1-12-1-1-100000000000000
χ232222-12-1-122-12-1-1-1-122-1-1-1-122222222-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-12-1-1-12-1-1-12-1-1-12-1-100000000000000
χ242222-12-1-122-12-1-1-1-122-1-1-1-12222-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-11-2111-2111-2111-21100000000000000
χ252222-12-1-122-12-1-1-1-122-1-1-1-1-2-2-2-222-2-2-12-1-1-12-1-111-2-2111111-2-21111-12-1-1-12-1-11-2111-21100000000000000
χ262222-12-1-122-12-1-1-1-122-1-1-1-1-2-2-2-2-2-222-12-1-1-12-1-111-2-2111111-2-211111-2111-211-12-1-1-12-1-100000000000000
χ272222-1-12-122-1-12-1-1-1-1-122-1-122222222-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-12-1-1-12-1-1-12-1-1-12-100000000000000
χ282222-1-12-122-1-12-1-1-1-1-122-1-12222-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-111-2111-2111-2111-2100000000000000
χ292222-1-12-122-1-12-1-1-1-1-122-1-1-2-2-2-222-2-2-1-12-1-1-12-11111-2-2111111-2-211-1-12-1-1-12-111-2111-2100000000000000
χ302222-1-12-122-1-12-1-1-1-1-122-1-1-2-2-2-2-2-222-1-12-1-1-12-11111-2-2111111-2-21111-2111-21-1-12-1-1-12-100000000000000
χ312222-1-1-1222-1-1-12-1-1-1-1-1-12222222222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-12-1-1-12-1-1-12-1-1-1200000000000000
χ322222-1-1-1222-1-1-12-1-1-1-1-1-1222222-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122111-2111-2111-2111-200000000000000
χ332222-1-1-1222-1-1-12-1-1-1-1-1-122-2-2-2-222-2-2-1-1-12-1-1-12111111-2-2111111-2-2-1-1-12-1-1-12111-2111-200000000000000
χ342222-1-1-1222-1-1-12-1-1-1-1-1-122-2-2-2-2-2-222-1-1-12-1-1-12111111-2-2111111-2-2111-2111-2-1-1-12-1-1-1200000000000000
χ3522-2-2222200-2-2-2-22-22-22-22-2i2−i2i2−i2000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000002-22-200i2−i2i2−i20000
χ3622-2-2222200-2-2-2-22-22-22-22-2i2−i2i2−i2000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000-22-2200−i2i2−i2i20000
χ3722-2-2222200-2-2-2-22-22-22-22-2−i2i2−i2i2000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000002-22-200−i2i2−i2i20000
χ3822-2-2222200-2-2-2-22-22-22-22-2−i2i2−i2i2000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000-22-2200i2−i2i2−i20000
χ392-22-2222200-2-2-2-2-22-22-22-22i2−i2−i2i2000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000000000002i−2i−2i2i00−222−20000
χ402-22-2222200-2-2-2-2-22-22-22-22i2−i2−i2i2000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000−2i2i2i−2i002−2−220000
χ412-22-2222200-2-2-2-2-22-22-22-22−i2i2i2−i2000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000000000002i−2i−2i2i002−2−220000
χ422-22-2222200-2-2-2-2-22-22-22-22−i2i2i2−i2000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000−2i2i2i−2i00−222−20000
χ432-2-222222-222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000000000000000000002i2i−2i−2i−2i2i00000000
χ442-2-222222-222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000000000000000000000−2i−2i2i2i2i−2i00000000
χ452-2-222-1-1-12-22-1-1-1-2-211111122-2-22i−2i2i−2i-21112-1-1-122-1-1-1-1-1-1-2-21111112i−i−i−i−2iiii2i−i−i−i−2iiii00000000000000
χ462-2-222-1-1-12-22-1-1-1-2-211111122-2-2−2i2i−2i2i-21112-1-1-122-1-1-1-1-1-1-2-2111111−2iiii2i−i−i−i−2iiii2i−i−i−i00000000000000
χ472-2-222-1-1-12-22-1-1-1-2-2111111-2-2222i−2i−2i2i-21112-1-1-1-2-211111122-1-1-1-1-1-12i−i−i−i−2iiii−2iiii2i−i−i−i00000000000000
χ482-2-222-1-1-12-22-1-1-1-2-2111111-2-222−2i2i2i−2i-21112-1-1-1-2-211111122-1-1-1-1-1-1−2iiii2i−i−i−i2i−i−i−i−2iiii00000000000000
χ492-2-22-12-1-12-2-12-1-111-2-2111122-2-22i−2i2i−2i1-211-12-1-1-1-122-1-1-1-111-2-21111−i2i−i−ii−2iii−i2i−i−ii−2iii00000000000000
χ502-2-22-12-1-12-2-12-1-111-2-2111122-2-2−2i2i−2i2i1-211-12-1-1-1-122-1-1-1-111-2-21111i−2iii−i2i−i−ii−2iii−i2i−i−i00000000000000
χ512-2-22-12-1-12-2-12-1-111-2-21111-2-2222i−2i−2i2i1-211-12-1-111-2-21111-1-122-1-1-1-1−i2i−i−ii−2iiii−2iii−i2i−i−i00000000000000
χ522-2-22-12-1-12-2-12-1-111-2-21111-2-222−2i2i2i−2i1-211-12-1-111-2-21111-1-122-1-1-1-1i−2iii−i2i−i−i−i2i−i−ii−2iii00000000000000
χ532-2-22-1-12-12-2-1-12-11111-2-21122-2-22i−2i2i−2i11-21-1-12-1-1-1-1-122-1-11111-2-211−i−i2i−iii−2ii−i−i2i−iii−2ii00000000000000
χ542-2-22-1-12-12-2-1-12-11111-2-21122-2-2−2i2i−2i2i11-21-1-12-1-1-1-1-122-1-11111-2-211ii−2ii−i−i2i−iii−2ii−i−i2i−i00000000000000
χ552-2-22-1-12-12-2-1-12-11111-2-211-2-2222i−2i−2i2i11-21-1-12-11111-2-211-1-1-1-122-1-1−i−i2i−iii−2iiii−2ii−i−i2i−i00000000000000
χ562-2-22-1-12-12-2-1-12-11111-2-211-2-222−2i2i2i−2i11-21-1-12-11111-2-211-1-1-1-122-1-1ii−2ii−i−i2i−i−i−i2i−iii−2ii00000000000000
χ572-2-22-1-1-122-2-1-1-12111111-2-222-2-22i−2i2i−2i111-2-1-1-12-1-1-1-1-1-122111111-2-2−i−i−i2iiii−2i−i−i−i2iiii−2i00000000000000
χ582-2-22-1-1-122-2-1-1-12111111-2-222-2-2−2i2i−2i2i111-2-1-1-12-1-1-1-1-1-122111111-2-2iii−2i−i−i−i2iiii−2i−i−i−i2i00000000000000
χ592-2-22-1-1-122-2-1-1-12111111-2-2-2-2222i−2i−2i2i111-2-1-1-12111111-2-2-1-1-1-1-1-122−i−i−i2iiii−2iiii−2i−i−i−i2i00000000000000
χ602-2-22-1-1-122-2-1-1-12111111-2-2-2-222−2i2i2i−2i111-2-1-1-12111111-2-2-1-1-1-1-1-122iii−2i−i−i−i2i−i−i−i2iiii−2i00000000000000
χ6144444-2-2-2-4-44-2-2-244-2-2-2-2-2-200000000-4222-42220000000000000000000000000000000000000000000000
χ624444-24-2-2-4-4-24-2-2-2-244-2-2-2-2000000002-4222-4220000000000000000000000000000000000000000000000
χ634444-2-24-2-4-4-2-24-2-2-2-2-244-2-20000000022-4222-420000000000000000000000000000000000000000000000
χ644444-2-2-24-4-4-2-2-24-2-2-2-2-2-24400000000222-4222-40000000000000000000000000000000000000000000000
χ6544-4-44-2-2-200-42224-4-22-22-222i2−2i22i2−2i20000000000002i2−2i2−i2i2−i2i2−i2i22i2−2i2−i2i2−i2i2−i2i2000000000000000000000000000000
χ6644-4-44-2-2-200-42224-4-22-22-22−2i22i2−2i22i2000000000000−2i22i2i2−i2i2−i2i2−i2−2i22i2i2−i2i2−i2i2−i2000000000000000000000000000000
χ6744-4-4-24-2-2002-422-224-4-22-222i2−2i22i2−2i2000000000000−i2i22i2−2i2−i2i2−i2i2−i2i22i2−2i2−i2i2−i2i2000000000000000000000000000000
χ6844-4-4-24-2-2002-422-224-4-22-22−2i22i2−2i22i2000000000000i2−i2−2i22i2i2−i2i2−i2i2−i2−2i22i2i2−i2i2−i2000000000000000000000000000000
χ6944-4-4-2-24-20022-42-22-224-4-222i2−2i22i2−2i2000000000000−i2i2−i2i22i2−2i2−i2i2−i2i2−i2i22i2−2i2−i2i2000000000000000000000000000000
χ7044-4-4-2-24-20022-42-22-224-4-22−2i22i2−2i22i2000000000000i2−i2i2−i2−2i22i2i2−i2i2−i2i2−i2−2i22i2i2−i2000000000000000000000000000000
χ7144-4-4-2-2-2400222-4-22-22-224-42i2−2i22i2−2i2000000000000−i2i2−i2i2−i2i22i2−2i2−i2i2−i2i2−i2i22i2−2i2000000000000000000000000000000
χ7244-4-4-2-2-2400222-4-22-22-224-4−2i22i2−2i22i2000000000000i2−i2i2−i2i2−i2−2i22i2i2−i2i2−i2i2−i2−2i22i2000000000000000000000000000000
χ734-44-44-2-2-200-4222-442-22-22-22i2−2i2−2i22i20000000000002i2−2i2−i2i2−i2i2−i2i2−2i22i2i2−i2i2−i2i2−i2000000000000000000000000000000
χ744-44-44-2-2-200-4222-442-22-22-2−2i22i22i2−2i2000000000000−2i22i2i2−i2i2−i2i2−i22i2−2i2−i2i2−i2i2−i2i2000000000000000000000000000000
χ754-44-4-24-2-2002-4222-2-442-22-22i2−2i2−2i22i2000000000000−i2i22i2−2i2−i2i2−i2i2i2−i2−2i22i2i2−i2i2−i2000000000000000000000000000000
χ764-44-4-24-2-2002-4222-2-442-22-2−2i22i22i2−2i2000000000000i2−i2−2i22i2i2−i2i2−i2−i2i22i2−2i2−i2i2−i2i2000000000000000000000000000000
χ774-44-4-2-24-20022-422-22-2-442-22i2−2i2−2i22i2000000000000−i2i2−i2i22i2−2i2−i2i2i2−i2i2−i2−2i22i2i2−i2000000000000000000000000000000
χ784-44-4-2-24-20022-422-22-2-442-2−2i22i22i2−2i2000000000000i2−i2i2−i2−2i22i2i2−i2−i2i2−i2i22i2−2i2−i2i2000000000000000000000000000000
χ794-44-4-2-2-2400222-42-22-22-2-442i2−2i2−2i22i2000000000000−i2i2−i2i2−i2i22i2−2i2i2−i2i2−i2i2−i2−2i22i2000000000000000000000000000000
χ804-44-4-2-2-2400222-42-22-22-2-44−2i22i22i2−2i2000000000000i2−i2i2−i2i2−i2−2i22i2−i2i2−i2i2−i2i22i2−2i2000000000000000000000000000000
χ814-4-444-2-2-2-444-2-2-2-4-4222222000000004-2-2-2-42220000000000000000000000000000000000000000000000
χ824-4-44-24-2-2-44-24-2-222-4-4222200000000-24-2-22-4220000000000000000000000000000000000000000000000
χ834-4-44-2-24-2-44-2-24-22222-4-42200000000-2-24-222-420000000000000000000000000000000000000000000000
χ844-4-44-2-2-24-44-2-2-24222222-4-400000000-2-2-24222-40000000000000000000000000000000000000000000000

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