Finite Group Databasebeta

← Group #10868356

Character table — Group #10868356

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order12222222344444444666666644444412121212121212122266668888121212121212242424242424242444448888888844121212122244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-111
χ511111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1
χ611111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-111
χ711111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-111111
χ811111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-111-1-1-1-1-1
χ91111111111-1-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111111-1-1-111-1-1-111111-1-1
χ101111111111-1-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-11-1-1-111111-1-1-1-1-111
χ111111111111-1-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1111-1-1-1-1-111-1-1111
χ121111111111-1-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-11111-1111-1-1111-1-111-1-1-1
χ131111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1111-1-111-1-1-1-1-1111
χ141111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1111-1-1-1-111111-1-1-1
χ151111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11-1-1-11111-1-1-1111-1-1
χ161111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111-1-1-111-1-1111-1-1-111
χ17222222222-22222-2-2-22222222-2-20000-2-22222-2-20000000000-2-200000000000022220000000000000000-20000-200
χ18222222222-22222-2-2-22222222-2-20000-2-22222-2-20000000000-2-2000000000000-2-2-2-2000000000000000020000200
χ19222222222-2-2-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-200000000002200000000000022-2-2000000000000000020000-200
χ20222222222-2-2-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-2000000000022000000000000-2-2220000000000000000-20000200
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
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2111122-2-211-1-1-1-1-1-1-1-111110000000000002-211-1-10000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-21111-2-22211-1-1-1-11111-1-1-1-1000000000000-22-1-1110000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-1-1-1-122-2-2111111-1-1-1-11111000000000000-22-1-1110000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-1-1-1-1-2-2221111111111-1-1-1-10000000000002-211-1-10000000000
χ29222-2-2-2-22222i2i−2i−2i-2-2222-2-2-22-22i−2i2i2i−2i−2i2-22i2i−2i−2i2-22-222-2-200002i−2i2i2i−2i−2i000000000000000000000000000000000000
χ30222-2-2-2-22222i2i−2i−2i-2-2222-2-2-22-22i−2i−2i−2i2i2i2-22i2i−2i−2i2-2-22-2-22200002i−2i−2i−2i2i2i000000000000000000000000000000000000
χ31222-2-2-2-2222−2i−2i2i2i-2-2222-2-2-22-2−2i2i2i2i−2i−2i2-2−2i−2i2i2i2-2-22-2-2220000−2i2i2i2i−2i−2i000000000000000000000000000000000000
χ32222-2-2-2-2222−2i−2i2i2i-2-2222-2-2-22-2−2i2i−2i−2i2i2i2-2−2i−2i2i2i2-22-222-2-20000−2i2i−2i−2i2i2i000000000000000000000000000000000000
χ33222-2-2-2-222-22i2i−2i−2i22-222-2-2-22-2−2i2i0000-222i2i−2i−2i-220000000000−2i2i0000000000000000000000000000002-202i−2i00000
χ34222-2-2-2-222-22i2i−2i−2i22-222-2-2-22-2−2i2i0000-222i2i−2i−2i-220000000000−2i2i000000000000000000000000000000-220−2i2i00000
χ35222-2-2-2-222-2−2i−2i2i2i22-222-2-2-22-22i−2i0000-22−2i−2i2i2i-2200000000002i−2i0000000000000000000000000000002-20−2i2i00000
χ36222-2-2-2-222-2−2i−2i2i2i22-222-2-2-22-22i−2i0000-22−2i−2i2i2i-2200000000002i−2i000000000000000000000000000000-2202i−2i00000
χ37222-2-2-2-22-122i2i−2i−2i-2-22-1-1111-112i−2i2i2i−2i−2i-11−i−iii-112-2-1-1110000−ii−i−iii33−3−3−i3−i3i3i3000000000000003−3−i3i30000000000
χ38222-2-2-2-22-122i2i−2i−2i-2-22-1-1111-112i−2i2i2i−2i−2i-11−i−iii-112-2-1-1110000−ii−i−iii−3−333i3i3−i3−i300000000000000−33i3−i30000000000
χ39222-2-2-2-22-122i2i−2i−2i-2-22-1-1111-112i−2i−2i−2i2i2i-11−i−iii-11-2211-1-10000−iiii−i−i33−3−3−i3−i3i3i300000000000000−33i3−i30000000000
χ40222-2-2-2-22-122i2i−2i−2i-2-22-1-1111-112i−2i−2i−2i2i2i-11−i−iii-11-2211-1-10000−iiii−i−i−3−333i3i3−i3−i3000000000000003−3−i3i30000000000
χ41222-2-2-2-22-12−2i−2i2i2i-2-22-1-1111-11−2i2i2i2i−2i−2i-11ii−i−i-11-2211-1-10000i−i−i−iii33−3−3i3i3−i3−i300000000000000−33−i3i30000000000
χ42222-2-2-2-22-12−2i−2i2i2i-2-22-1-1111-11−2i2i2i2i−2i−2i-11ii−i−i-11-2211-1-10000i−i−i−iii−3−333−i3−i3i3i3000000000000003−3i3−i30000000000
χ43222-2-2-2-22-12−2i−2i2i2i-2-22-1-1111-11−2i2i−2i−2i2i2i-11ii−i−i-112-2-1-1110000i−iii−i−i33−3−3i3i3−i3−i3000000000000003−3i3−i30000000000
χ44222-2-2-2-22-12−2i−2i2i2i-2-22-1-1111-11−2i2i−2i−2i2i2i-11ii−i−i-112-2-1-1110000i−iii−i−i−3−333−i3−i3i3i300000000000000−33−i3i30000000000
χ4522-222-2-2-22200002-2-2-2-2-22-222002-22-22-20000-220000000000002-22-200000000000000002i2i−2i−2i000000000002i−2i000
χ4622-222-2-2-22200002-2-2-2-2-22-222002-22-22-20000-220000000000002-22-20000000000000000−2i−2i2i2i00000000000−2i2i000
χ4722-222-2-2-22200002-2-2-2-2-22-22200-22-222-20000-22000000000000-22-2200000000000000002i2i−2i−2i00000000000−2i2i000
χ4822-222-2-2-22200002-2-2-2-2-22-22200-22-222-20000-22000000000000-22-220000000000000000−2i−2i2i2i000000000002i−2i000
χ4922-2-2-222-2220000-22-2-2-22-222-2002i−2i−2i2i220000-2-20000000000002i−2i−2i2i00000000000022-2-20000000000000000002i−2i
χ5022-2-2-222-2220000-22-2-2-22-222-2002i−2i−2i2i220000-2-20000000000002i−2i−2i2i000000000000-2-222000000000000000000−2i2i
χ5122-2-2-222-2220000-22-2-2-22-222-200−2i2i2i−2i220000-2-2000000000000−2i2i2i−2i00000000000022-2-2000000000000000000−2i2i
χ5222-2-2-222-2220000-22-2-2-22-222-200−2i2i2i−2i220000-2-2000000000000−2i2i2i−2i000000000000-2-2220000000000000000002i−2i
χ532-22-222-2-2202-22-20002-22-2-2-22000000002-22-200000000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i22-22-2−i2i2−i2i2−i2i2−i2i20000000000000000
χ542-22-222-2-2202-22-20002-22-2-2-22000000002-22-200000000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i2-22-22i2−i2i2−i2i2−i2i2−i20000000000000000
χ552-22-222-2-2202-22-20002-22-2-2-22000000002-22-200000000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i22-22-2i2−i2i2−i2i2−i2i2−i20000000000000000
χ562-22-222-2-2202-22-20002-22-2-2-22000000002-22-200000000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i2-22-22−i2i2−i2i2−i2i2−i2i20000000000000000
χ572-22-222-2-220-22-220002-22-2-2-2200000000-22-2200000000−i2i2i2−i2000000−i2i2−i2i2i2−i2i2−i22-2-22i2−i2i2−i2−i2i2−i2i20000000000000000
χ582-22-222-2-220-22-220002-22-2-2-2200000000-22-2200000000−i2i2i2−i2000000−i2i2−i2i2i2−i2i2−i2-222-2−i2i2−i2i2i2−i2i2−i20000000000000000
χ592-22-222-2-220-22-220002-22-2-2-2200000000-22-2200000000i2−i2−i2i2000000i2−i2i2−i2−i2i2−i2i22-2-22−i2i2−i2i2i2−i2i2−i20000000000000000
χ602-22-222-2-220-22-220002-22-2-2-2200000000-22-2200000000i2−i2−i2i2000000i2−i2i2−i2−i2i2−i2i2-222-2i2−i2i2−i2−i2i2−i2i20000000000000000
χ6144444444-2-44444-4-4-4-2-2-2-2-2-2-2-4-4000022-2-2-2-2220000000000220000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2440000222222220000000000-2-20000000000000000000000000000000000000000
χ63444-4-4-4-44-2-44i4i−4i−4i44-4-2-2222-22−4i4i00002-2−2i−2i2i2i2-200000000002i−2i0000000000000000000000000000000000000000
χ64444-4-4-4-44-2-4−4i−4i4i4i44-4-2-2222-224i−4i00002-22i2i−2i−2i2-20000000000−2i2i0000000000000000000000000000000000000000
χ6544-444-4-4-44-40000-444-4-4-44-444000000-4400004-40000000000000000000000000000000000000000000000000000
χ6644-444-4-4-4-2400004-4-4222-22-2-2004-44-4-2200002-2000000000000-22-22000000000000000000000000000000000000
χ6744-444-4-4-4-2400004-4-4222-22-2-200-44-44-2200002-20000000000002-22-2000000000000000000000000000000000000
χ6844-444-4-4-4-2-40000-444222-22-2-20000002-20000-2200−2i32i3−2i32i30000000000000000000000000000000000000000000000
χ6944-444-4-4-4-2-40000-444222-22-2-20000002-20000-22002i3−2i32i3−2i30000000000000000000000000000000000000000000000
χ7044-4-4-444-44-400004-44-4-44-444-4000000-4-40000440000000000000000000000000000000000000000000000000000
χ7144-4-4-444-4-240000-44-422-22-2-22004i−4i−4i4i-2-2000022000000000000−2i2i2i−2i000000000000000000000000000000000000
χ7244-4-4-444-4-240000-44-422-22-2-2200−4i4i4i−4i-2-20000220000000000002i−2i−2i2i000000000000000000000000000000000000
χ7344-4-4-444-4-2-400004-4422-22-2-22000000220000-2-200−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ7444-4-4-444-4-2-400004-4422-22-2-22000000220000-2-2002i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ754-444-4-44-4404i−4i−4i4i0004-4-444-4-4000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ764-444-4-44-440−4i4i4i−4i0004-4-444-4-400000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ774-444-4-44-4-204i−4i−4i4i000-222-2-22200000000−2i2i2i−2i000000000000000000i6−i6−i6i66−6−660000000000000000000000000000
χ784-444-4-44-4-204i−4i−4i4i000-222-2-22200000000−2i2i2i−2i000000000000000000−i6i6i6−i6−666−60000000000000000000000000000
χ794-444-4-44-4-20−4i4i4i−4i000-222-2-222000000002i−2i−2i2i000000000000000000i6−i6−i6i6−666−60000000000000000000000000000
χ804-444-4-44-4-20−4i4i4i−4i000-222-2-222000000002i−2i−2i2i000000000000000000−i6i6i6−i66−6−660000000000000000000000000000
χ814-44-444-4-4-204-44-4000-22-2222-200000000-22-2200000000−2i22i2−2i22i2000000i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ824-44-444-4-4-204-44-4000-22-2222-200000000-22-22000000002i2−2i22i2−2i2000000−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ834-44-444-4-4-20-44-44000-22-2222-2000000002-22-200000000−2i22i22i2−2i2000000i2−i2i2−i2−i2i2−i2i20000000000000000000000000000
χ844-44-444-4-4-20-44-44000-22-2222-2000000002-22-2000000002i2−2i2−2i22i2000000−i2i2−i2i2i2−i2i2−i20000000000000000000000000000
χ854-4-44-44-44400000000-4444-4-4-4000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ864-4-44-44-44400000000-4444-4-4-40000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ874-4-4-44-444400000000-44-4-44-44000000000000000000000000000000000000000000000022−22−22220000000000000000
χ884-4-4-44-444400000000-44-4-44-440000000000000000000000000000000000000000000000−222222−220000000000000000
χ898-8-88-88-88-4000000004-4-4-4444000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-88-888-4000000004-444-44-4000000000000000000000000000000000000000000000000000000000000000000

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