Finite Group Databasebeta

← Group #10828776

Character table — Group #10828776

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order1222222234444444466666662244441212121212121212446688881212121212121212242424242424242422448888888844121212122244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-111
χ811111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1
χ91111111111-1-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-111-1-1-1-11-11111-1-1
χ101111111111-1-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-111-1-111-11-1-1-1-111
χ111111111111-1-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-1-111-1-11-1-1-11111
χ121111111111-1-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-11-1-11111-1111-1-1-1-1
χ131111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-11-1-111111-1-1-1-1-111
χ141111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-11-1-111-1-1-111111-1-1
χ151111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111111-111-1-1111-111-1-1-1-1
χ161111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-11-111-1-1-1-1-11-1-11111
χ17222222222-22222-2-2-22222222-2-20000-2-22222-2-200-2-20000000000000000000022220000000000000000-2-2000000
χ18222222222-22222-2-2-22222222-2-20000-2-22222-2-200-2-200000000000000000000-2-2-2-2000000000000000022000000
χ19222222222-2-2-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-200220000000000000000000022-2-20000000000000000-22000000
χ20222222222-2-2-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-2002200000000000000000000-2-22200000000000000002-2000000
χ2122222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1222211111111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1-2-2-2-2111111111111111100000000000022-1-1-1-10000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-21122-2-2-1-1-1-11111-1-1-1-111110000000000002-2-1-1110000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-211-2-222-1-1-1-111111111-1-1-1-1000000000000-2211-1-10000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1221122-2-21111-1-1-1-1-1-1-1-11111000000000000-2211-1-10000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-12211-2-2221111-1-1-1-11111-1-1-1-10000000000002-2-1-1110000000000
χ2922-22-22-2-22-200002-222-222-2-2-2002i2i−2i−2i2-200002-2000000002i2i−2i−2i000000000000000022-2-2000000000000002i−2i0000
χ3022-22-22-2-22-200002-222-222-2-2-2002i2i−2i−2i2-200002-2000000002i2i−2i−2i0000000000000000-2-22200000000000000−2i2i0000
χ3122-22-22-2-22-200002-222-222-2-2-200−2i−2i2i2i2-200002-200000000−2i−2i2i2i000000000000000022-2-200000000000000−2i2i0000
χ3222-22-22-2-22-200002-222-222-2-2-200−2i−2i2i2i2-200002-200000000−2i−2i2i2i0000000000000000-2-222000000000000002i−2i0000
χ3322-2-22-22-2202i2i−2i−2i0002-2-2-222-2000000002i2i−2i−2i000000−i2i22−200000000−i2−i2i2i222−2−22-22i−2i−i2i2−i2i222−2−20000000000000000
χ3422-2-22-22-2202i2i−2i−2i0002-2-2-222-2000000002i2i−2i−2i000000−i2i22−200000000−i2−i2i2i222−2−2-22−2i2ii2−i2i2−i2−2−2220000000000000000
χ3522-2-22-22-2202i2i−2i−2i0002-2-2-222-2000000002i2i−2i−2i000000i2−i2−2200000000i2i2−i2−i2−2−2222-22i−2ii2−i2i2−i2−2−2220000000000000000
χ3622-2-22-22-2202i2i−2i−2i0002-2-2-222-2000000002i2i−2i−2i000000i2−i2−2200000000i2i2−i2−i2−2−222-22−2i2i−i2i2−i2i222−2−20000000000000000
χ3722-2-22-22-220−2i−2i2i2i0002-2-2-222-200000000−2i−2i2i2i000000−i2i2−2200000000−i2−i2i2i2−2−2222-2−2i2i−i2i2−i2i2−2−2220000000000000000
χ3822-2-22-22-220−2i−2i2i2i0002-2-2-222-200000000−2i−2i2i2i000000−i2i2−2200000000−i2−i2i2i2−2−222-222i−2ii2−i2i2−i222−2−20000000000000000
χ3922-2-22-22-220−2i−2i2i2i0002-2-2-222-200000000−2i−2i2i2i000000i2−i22−200000000i2i2−i2−i222−2−22-2−2i2ii2−i2i2−i222−2−20000000000000000
χ4022-2-22-22-220−2i−2i2i2i0002-2-2-222-200000000−2i−2i2i2i000000i2−i22−200000000i2i2−i2−i222−2−2-222i−2i−i2i2−i2i2−2−2220000000000000000
χ412-22-222-2-22-20000-222-222-22-2-2002i−2i2i−2i2-20000-22000000002i−2i2i−2i000000000000000000002-22-2000000000000002i−2i
χ422-22-222-2-22-20000-222-222-22-2-2002i−2i2i−2i2-20000-22000000002i−2i2i−2i00000000000000000000-22-2200000000000000−2i2i
χ432-22-222-2-22-20000-222-222-22-2-200−2i2i−2i2i2-20000-2200000000−2i2i−2i2i000000000000000000002-22-200000000000000−2i2i
χ442-22-222-2-22-20000-222-222-22-2-200−2i2i−2i2i2-20000-2200000000−2i2i−2i2i00000000000000000000-22-22000000000000002i−2i
χ452-2-2-2-2222222-22-2-2-22-2-22-2-2222-22-2-22222-22-2-2-22-22-200002-2-2222-2-2000000000000000000000000000000000000
χ462-2-2-2-2222222-22-2-2-22-2-22-2-2222-2-222-2222-22-2-2-2-222-20000-222-2-2-222000000000000000000000000000000000000
χ472-2-2-2-222222-22-22-2-22-2-22-2-222-222-2-2222-22-22-2-2-22-2200002-2-22-2-222000000000000000000000000000000000000
χ482-2-2-2-222222-22-22-2-22-2-22-2-222-22-222-222-22-22-2-22-2-220000-222-222-2-2000000000000000000000000000000000000
χ492-2-2-2-22222-22-22-222-2-2-22-2-222-220000-2-22-22-22200-22000000000000000000000000000000000000002-200002-200
χ502-2-2-2-22222-22-22-222-2-2-22-2-222-220000-2-22-22-22200-2200000000000000000000000000000000000000-220000-2200
χ512-2-2-2-22222-2-22-2222-2-2-22-2-2222-20000-2-2-22-2222002-2000000000000000000000000000000000000002-20000-2200
χ522-2-2-2-22222-2-22-2222-2-2-22-2-2222-20000-2-2-22-2222002-200000000000000000000000000000000000000-2200002-200
χ532-2-2-2-2222-122-22-2-2-2211-111-1-12-22-2-22-1-1-11-11112-2-110000-111-1-1-1113−33−33−33−3000000000000003−33−30000000000
χ542-2-2-2-2222-122-22-2-2-2211-111-1-12-22-2-22-1-1-11-11112-2-110000-111-1-1-111−33−33−33−3300000000000000−33−330000000000
χ552-2-2-2-2222-122-22-2-2-2211-111-1-12-2-222-2-1-1-11-1111-22-1100001-1-1111-1-13−33−33−33−300000000000000−33−330000000000
χ562-2-2-2-2222-122-22-2-2-2211-111-1-12-2-222-2-1-1-11-1111-22-1100001-1-1111-1-1−33−33−33−33000000000000003−33−30000000000
χ572-2-2-2-2222-12-22-22-2-2211-111-1-1-222-2-22-1-11-11-111-221-10000-111-111-1-13−33−3−33−33000000000000003−3−330000000000
χ582-2-2-2-2222-12-22-22-2-2211-111-1-1-222-2-22-1-11-11-111-221-10000-111-111-1-1−33−333−33−300000000000000−333−30000000000
χ592-2-2-2-2222-12-22-22-2-2211-111-1-1-22-222-2-1-11-11-1112-21-100001-1-11-1-1113−33−3−33−3300000000000000−333−30000000000
χ602-2-2-2-2222-12-22-22-2-2211-111-1-1-22-222-2-1-11-11-1112-21-100001-1-11-1-111−33−333−33−3000000000000003−3−330000000000
χ6144444444-2-44444-4-4-4-2-2-2-2-2-2-2-4-4000022-2-2-2-2220022000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24400002222222200-2-2000000000000000000000000000000000000000000000000
χ63444-4-4-4-4440000000044-4-4-4-44000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ64444-4-4-4-4440000000044-4-4-4-440000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ6544-44-44-4-4440000-44-44-444-4-4-4000000-440000-440000000000000000000000000000000000000000000000000000
χ6644-44-44-4-4-240000-44-4-22-2-22220000002-200002-200000000000023−2323−23000000000000000000000000000000000000
χ6744-44-44-4-4-240000-44-4-22-2-22220000002-200002-2000000000000−2323−2323000000000000000000000000000000000000
χ6844-44-44-4-4-2-400004-44-22-2-2222004i4i−4i−4i-220000-2200000000−2i−2i2i2i0000000000000000000000000000000000000000
χ6944-44-44-4-4-2-400004-44-22-2-222200−4i−4i4i4i-220000-22000000002i2i−2i−2i0000000000000000000000000000000000000000
χ7044-4-44-44-4-204i4i−4i−4i000-2222-2-2200000000−2i−2i2i2i000000−2i22i222−2200000000i2i2−i2−i2−2−2220000000000000000000000000000
χ7144-4-44-44-4-204i4i−4i−4i000-2222-2-2200000000−2i−2i2i2i0000002i2−2i2−222200000000−i2−i2i2i222−2−20000000000000000000000000000
χ7244-4-44-44-4-20−4i−4i4i4i000-2222-2-22000000002i2i−2i−2i000000−2i22i2−222200000000i2i2−i2−i222−2−20000000000000000000000000000
χ7344-4-44-44-4-20−4i−4i4i4i000-2222-2-22000000002i2i−2i−2i0000002i2−2i222−2200000000−i2−i2i2i2−2−2220000000000000000000000000000
χ744-444-4-44-4404i−4i−4i4i000-44-44-44-4000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ754-444-4-44-440−4i4i4i−4i000-44-44-44-400000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ764-444-4-44-4-204i−4i−4i4i0002-22-22-2200000000−2i2i2i−2i000000000000000000i6−i6−i6i6−666−60000000000000000000000000000
χ774-444-4-44-4-204i−4i−4i4i0002-22-22-2200000000−2i2i2i−2i000000000000000000−i6i6i6−i66−6−660000000000000000000000000000
χ784-444-4-44-4-20−4i4i4i−4i0002-22-22-22000000002i−2i−2i2i000000000000000000i6−i6−i6i66−6−660000000000000000000000000000
χ794-444-4-44-4-20−4i4i4i−4i0002-22-22-22000000002i−2i−2i2i000000000000000000−i6i6i6−i6−666−60000000000000000000000000000
χ804-44-444-4-44400004-4-4-444-44-4-4000000-4400004-40000000000000000000000000000000000000000000000000000
χ814-44-444-4-4-2400004-4-42-2-22-2220000002-20000-2200000000000023−23−2323000000000000000000000000000000000000
χ824-44-444-4-4-2400004-4-42-2-22-2220000002-20000-22000000000000−232323−23000000000000000000000000000000000000
χ834-44-444-4-4-2-40000-4442-2-22-222004i−4i4i−4i-2200002-200000000−2i2i−2i2i0000000000000000000000000000000000000000
χ844-44-444-4-4-2-40000-4442-2-22-22200−4i4i−4i4i-2200002-2000000002i−2i2i−2i0000000000000000000000000000000000000000
χ854-4-444-4-44400000000-4-4-444-44000000000000000000000000000000000000000000000022−22−22220000000000000000
χ864-4-444-4-44400000000-4-4-444-440000000000000000000000000000000000000000000000−222222−220000000000000000
χ874-4-4-4-4444-2-44-44-444-422-222-2-2-44000022-22-22-2-2002-2000000000000000000000000000000000000000000000000
χ884-4-4-4-4444-2-4-44-4444-422-222-2-24-40000222-22-2-2-200-22000000000000000000000000000000000000000000000000
χ89888-8-8-8-88-400000000-4-44444-4000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-8-88-400000000444-4-44-4000000000000000000000000000000000000000000000000000000000000000000

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