Finite Group Databasebeta

← Group #10849227

Character table — Group #10849227

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order12222222344444444666666644444412121212121212122266668888121212121212242424242424242444448888888844121212124444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ411111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ511111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ611111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ711111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ811111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111
χ91111111111-1-1-1-11111111111-1-11111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-11-111-1-111-1-11-111-1-1
χ101111111111-1-1-1-11111111111-1-11111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111-111-1-1-1-111-11-1-111
χ111111111111-1-1-1-11111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-11111-11-1-111-1-1111-111-1-1
χ121111111111-1-1-1-11111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1111111-1-1-1-1-11-1-11111-1-1-11-1-111
χ131111111111-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-11-1-111-1-1111-1-1-111
χ141111111111-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-1-1111-1-1
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-111-1-111-1-11-1-1-111
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11-111-1-1-1-111-1111-1-1
χ17222222222-22222-2-2-22222222-2-20000-2-2-22222-20000000000-2-20000000000002222000000000000000000-2-20000
χ18222222222-22222-2-2-22222222-2-20000-2-2-22222-20000000000-2-2000000000000-2-2-2-2000000000000000000220000
χ19222222222-2-2-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-200000000002200000000000022-2-2000000000000000000-220000
χ20222222222-2-2-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-2000000000022000000000000-2-2220000000000000000002-20000
χ2122222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-211112222-1-11111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-21111-2-2-2-2-1-111111111111100000000000022-1-1-1-10000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-1-1-11111-1-2-2111122-2-211-1-1-1-1-1-1-1-111110000000000002-2-1-1110000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-1-1-11111-1-2-21111-2-22211-1-1-1-11111-1-1-1-1000000000000-2211-1-10000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-122-1-1-1-122-2-2111111-1-1-1-11111000000000000-2211-1-10000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-122-1-1-1-1-2-2221111111111-1-1-1-10000000000002-2-1-1110000000000
χ29222-2-2-22-22022-2-200022-2-2-2-2200000000022-2-200000002−22−200000022−2−222−2−22i−2i2i−2i−i2−i2i2i2−i2−i2i2i20000000000000000
χ30222-2-2-22-22022-2-200022-2-2-2-2200000000022-2-200000002−22−200000022−2−222−2−2−2i2i−2i2ii2i2−i2−i2i2i2−i2−i20000000000000000
χ31222-2-2-22-22022-2-200022-2-2-2-2200000000022-2-20000000−22−22000000−2−222−2−2222i−2i2i−2ii2i2−i2−i2i2i2−i2−i20000000000000000
χ32222-2-2-22-22022-2-200022-2-2-2-2200000000022-2-20000000−22−22000000−2−222−2−222−2i2i−2i2i−i2−i2i2i2−i2−i2i2i20000000000000000
χ33222-2-2-22-220-2-22200022-2-2-2-22000000000-2-22200000002−2−2200000022−2−2−2−2222i−2i−2i2i−i2−i2i2i2i2i2−i2−i20000000000000000
χ34222-2-2-22-220-2-22200022-2-2-2-22000000000-2-22200000002−2−2200000022−2−2−2−222−2i2i2i−2ii2i2−i2−i2−i2−i2i2i20000000000000000
χ35222-2-2-22-220-2-22200022-2-2-2-22000000000-2-2220000000−222−2000000−2−22222−2−22i−2i−2i2ii2i2−i2−i2−i2−i2i2i20000000000000000
χ36222-2-2-22-220-2-22200022-2-2-2-22000000000-2-2220000000−222−2000000−2−22222−2−2−2i2i2i−2i−i2−i2i2i2i2i2−i2−i20000000000000000
χ3722-22-2-2-222-2000022-22-22-22-2-2002i2i−2i−2i2-2-2000020000000000002i2i−2i−2i00000000000000002i−2i2i−2i000000002-2000000
χ3822-22-2-2-222-2000022-22-22-22-2-2002i2i−2i−2i2-2-2000020000000000002i2i−2i−2i0000000000000000−2i2i−2i2i00000000-22000000
χ3922-22-2-2-222-2000022-22-22-22-2-200−2i−2i2i2i2-2-200002000000000000−2i−2i2i2i00000000000000002i−2i2i−2i00000000-22000000
χ4022-22-2-2-222-2000022-22-22-22-2-200−2i−2i2i2i2-2-200002000000000000−2i−2i2i2i0000000000000000−2i2i−2i2i000000002-2000000
χ412-22-22-2-222-200002-22-22-222-2-2002i−2i2i−2i-22-2000020000000000002i−2i2i−2i0000000000002i−2i2i−2i00000000002-200000000
χ422-22-22-2-222-200002-22-22-222-2-2002i−2i2i−2i-22-2000020000000000002i−2i2i−2i000000000000−2i2i−2i2i0000000000-2200000000
χ432-22-22-2-222-200002-22-22-222-2-200−2i2i−2i2i-22-200002000000000000−2i2i−2i2i0000000000002i−2i2i−2i0000000000-2200000000
χ442-22-22-2-222-200002-22-22-222-2-200−2i2i−2i2i-22-200002000000000000−2i2i−2i2i000000000000−2i2i−2i2i00000000002-200000000
χ452-2-2-2-2222222-22-22-2-2-2-2-2-22222-22-2-22-2-222-22-222-222-2-200002-22-2-22000000000000000000000000000000000000
χ462-2-2-2-2222222-22-22-2-2-2-2-2-22222-2-222-2-2-222-22-22-22-2-22200002-2-222-2000000000000000000000000000000000000
χ472-2-2-2-222222-22-222-2-2-2-2-2-2222-222-2-22-2-22-22-222-22-2-2220000-222-2-22000000000000000000000000000000000000
χ482-2-2-2-222222-22-222-2-2-2-2-2-2222-22-222-2-2-22-22-2222-222-2-20000-22-222-2000000000000000000000000000000000000
χ492-2-2-2-22222-22-22-2-222-2-2-2-2222-22000022-22-22-2-20000000000-220000000000000000000000000000000000002-22-2
χ502-2-2-2-22222-22-22-2-222-2-2-2-2222-22000022-22-22-2-20000000000-22000000000000000000000000000000000000-22-22
χ512-2-2-2-22222-2-22-22-222-2-2-2-22222-2000022-2-22-22-200000000002-20000000000000000000000000000000000002-2-22
χ522-2-2-2-22222-2-22-22-222-2-2-2-22222-2000022-2-22-22-200000000002-2000000000000000000000000000000000000-222-2
χ532-2-2-2-2222-122-22-22-2-21111-1-1-12-22-2-2211-1-11-11-12-2-1-1110000-11-111-1−i3i3−i3i3−i3i3−i3i300000000000000−i3i3−i3i30000000000
χ542-2-2-2-2222-122-22-22-2-21111-1-1-12-22-2-2211-1-11-11-12-2-1-1110000-11-111-1i3−i3i3−i3i3−i3i3−i300000000000000i3−i3i3−i30000000000
χ552-2-2-2-2222-122-22-22-2-21111-1-1-12-2-222-211-1-11-11-1-2211-1-10000-111-1-11−i3i3−i3i3−i3i3−i3i300000000000000i3−i3i3−i30000000000
χ562-2-2-2-2222-122-22-22-2-21111-1-1-12-2-222-211-1-11-11-1-2211-1-10000-111-1-11i3−i3i3−i3i3−i3i3−i300000000000000−i3i3−i3i30000000000
χ572-2-2-2-2222-12-22-222-2-21111-1-1-1-222-2-2211-11-11-1-1-2211-1-100001-1-111-1−i3i3−i3i3i3−i3i3−i300000000000000−i3i3i3−i30000000000
χ582-2-2-2-2222-12-22-222-2-21111-1-1-1-222-2-2211-11-11-1-1-2211-1-100001-1-111-1i3−i3i3−i3−i3i3−i3i300000000000000i3−i3−i3i30000000000
χ592-2-2-2-2222-12-22-222-2-21111-1-1-1-22-222-211-11-11-1-12-2-1-11100001-11-1-11−i3i3−i3i3i3−i3i3−i300000000000000i3−i3−i3i30000000000
χ602-2-2-2-2222-12-22-222-2-21111-1-1-1-22-222-211-11-11-1-12-2-1-11100001-11-1-11i3−i3i3−i3−i3i3−i3i300000000000000−i3i3i3−i30000000000
χ6144444444-2-44444-4-4-4-2-2-2-2-2-2-2-4-40000222-2-2-2-220000000000220000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2440000222222220000000000-2-20000000000000000000000000000000000000000
χ63444-4-4-44-4-2044-4-4000-2-22222-2000000000-2-222000000022−2222−22000000−2−222−2−2220000000000000000000000000000
χ64444-4-4-44-4-2044-4-4000-2-22222-2000000000-2-2220000000−2222−222200000022−2−222−2−20000000000000000000000000000
χ65444-4-4-44-4-20-4-444000-2-22222-200000000022-2-2000000022−22−2222000000−2−22222−2−20000000000000000000000000000
χ66444-4-4-44-4-20-4-444000-2-22222-200000000022-2-20000000−222222−2200000022−2−2−2−2220000000000000000000000000000
χ6744-44-4-4-44440000-4-444-44-44-4-4000000-4440000-40000000000000000000000000000000000000000000000000000
χ6844-44-4-4-44-240000-4-44-22-22-2220000002-2-20000200−2i32i3−2i32i30000000000000000000000000000000000000000000000
χ6944-44-4-4-44-240000-4-44-22-22-2220000002-2-200002002i3−2i32i3−2i30000000000000000000000000000000000000000000000
χ7044-44-4-4-44-2-4000044-4-22-22-222004i4i−4i−4i-2220000-2000000000000−2i−2i2i2i000000000000000000000000000000000000
χ7144-44-4-4-44-2-4000044-4-22-22-22200−4i−4i4i4i-2220000-20000000000002i2i−2i−2i000000000000000000000000000000000000
χ7244-4-444-4-44000000004-4-44-44-4000000000000000000000000000000000000000000000022−22−22220000000000000000
χ7344-4-444-4-44000000004-4-44-44-40000000000000000000000000000000000000000000000−222222−220000000000000000
χ744-444-44-4-4400000000-444-4-44-400000000000000000000000000000000000000000022−22−222200000000000000000000
χ754-444-44-4-4400000000-444-4-44-4000000000000000000000000000000000000000000−222222−2200000000000000000000
χ764-44-44-4-44440000-44-4-44-444-4-40000004-440000-40000000000000000000000000000000000000000000000000000
χ774-44-44-4-44-240000-44-42-22-2-222000000-22-20000200−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ784-44-44-4-44-240000-44-42-22-2-222000000-22-200002002i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ794-44-44-4-44-2-400004-442-22-2-222004i−4i4i−4i2-220000-2000000000000−2i2i−2i2i000000000000000000000000000000000000
χ804-44-44-4-44-2-400004-442-22-2-22200−4i4i−4i4i2-220000-20000000000002i−2i2i−2i000000000000000000000000000000000000
χ814-4-444-44-4404-4-44000-4-444-4-440000000004-4-4400000000000000000000000000000000000000000000000000000
χ824-4-444-44-440-444-4000-4-444-4-44000000000-444-400000000000000000000000000000000000000000000000000000
χ834-4-444-44-4-204-4-4400022-2-222-2000000000-222-200000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ844-4-444-44-4-204-4-4400022-2-222-2000000000-222-200000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ854-4-444-44-4-20-444-400022-2-222-20000000002-2-2200000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ864-4-444-44-4-20-444-400022-2-222-20000000002-2-2200000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ874-4-4-4-4444-2-44-44-4-4442222-2-2-2-440000-2-22-22-22200000000002-20000000000000000000000000000000000000000
χ884-4-4-4-4444-2-4-44-44-4442222-2-2-24-40000-2-222-22-220000000000-220000000000000000000000000000000000000000
χ8988-8-888-8-8-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000000000
χ908-888-88-8-8-4000000004-4-444-44000000000000000000000000000000000000000000000000000000000000000000

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