Finite Group Databasebeta

← Group #10690000

Character table — Group #10690000

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order122222223444444446666666444444121212121212121244888812121212121212121212242424242424242444448888888844121212122244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ81111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1
χ91-111-1-11-111-1-111-1-11-1-111-1-111ii−i−i-111-1-111-1-1i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i1-111-1-11-1ii−i−i11-1-1
χ101-111-1-11-111-1-111-1-11-1-111-1-111ii−i−i-111-1-111-1-1i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−i−i−i−iiiii1-111-1-1-11−i−iii-1-111
χ111-111-1-11-111-1-111-1-11-1-111-1-111ii−i−i-111-1-111-1-1i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−i−i−iiiii-11-1-1111-1ii−i−i-1-111
χ121-111-1-11-111-1-111-1-11-1-111-1-111ii−i−i-111-1-111-1-1i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiii-1-111iiii−i−i−i−i-11-1-111-11−i−iii11-1-1
χ131-111-1-11-111-1-111-1-11-1-111-1-111−i−iii-111-1-111-1-1−iiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1iiii−i−i−i−i-11-1-1111-1−i−iii-1-111
χ141-111-1-11-111-1-111-1-11-1-111-1-111−i−iii-111-1-111-1-1−iiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−i−i−iiiii-11-1-111-11ii−i−i11-1-1
χ151-111-1-11-111-1-111-1-11-1-111-1-111−i−iii-111-1-111-1-1−ii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−i−i−iiiii1-111-1-11-1−i−iii11-1-1
χ161-111-1-11-111-1-111-1-11-1-111-1-111−i−iii-111-1-111-1-1−ii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii-1-111iiii−i−i−i−i1-111-1-1-11ii−i−i-1-111
χ17222222222222-2-2-2-222222222-20000-22222-2-2-2-2000000-2-20000000000000000222200000000000000-2-200000000
χ18222222222222-2-2-2-222222222-20000-22222-2-2-2-2000000-2-20000000000000000-2-2-2-2000000000000002200000000
χ19222222222-2-2-22222-22222222-22222-2-2-2-2-22222-2-20000-2-222-2-222-2-2000000000000000000000000000000000000
χ20222222222-2-2-22222-22222222-2-2-2-2-2-2-2-2-2-22222220000-2-2-2-222-2-222000000000000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-22222222200002-2-2-2-2-2-2-2-2000000220000000000000000000000000000000000002-22-20000
χ22222222222-2-2-2-2-2-2-2-22222222200002-2-2-2-2-2-2-2-200000022000000000000000000000000000000000000-22-220000
χ2322222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ2422222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-211110000000000
χ2522222222-122222222-1-1-1-1-1-1-12-2-2-2-22-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ2622222222-122222222-1-1-1-1-1-1-12-2-2-2-22-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1111111111111111100000000000022-1-1-1-10000000000
χ2722222222-1-2-2-22222-2-1-1-1-1-1-1-1-22222-21111-1-1-1-1-2-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ2822222222-1-2-2-22222-2-1-1-1-1-1-1-1-22222-21111-1-1-1-1-2-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ2922222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12200001111-1-111-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ3022222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12200001111-1-111-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ31222-2-2-2-222-22-200002222-2-2-2-20000002-22-20000002−22−200000000002−22−22−22−22i−2i2i−2i−i2−i2i2i2−i2−i2i2i20000000000000000
χ32222-2-2-2-222-22-200002222-2-2-2-20000002-22-20000002−22−200000000002−22−22−22−2−2i2i−2i2ii2i2−i2−i2i2i2−i2−i20000000000000000
χ33222-2-2-2-222-22-200002222-2-2-2-20000002-22-2000000−22−220000000000−22−22−22−222i−2i2i−2ii2i2−i2−i2i2i2−i2−i20000000000000000
χ34222-2-2-2-222-22-200002222-2-2-2-20000002-22-2000000−22−220000000000−22−22−22−22−2i2i−2i2i−i2−i2i2i2−i2−i2i2i20000000000000000
χ3522-2-22-22-220002-22-202-2-2-22-2202i−2i2i−2i000002-22-2000000002i−2i002i−2i00000000000000−i2i2−i2i2−i2i2−i2i20000000000002−22−2
χ3622-2-22-22-220002-22-202-2-2-22-2202i−2i2i−2i000002-22-2000000002i−2i002i−2i00000000000000i2−i2i2−i2i2−i2i2−i2000000000000−22−22
χ3722-2-22-22-220002-22-202-2-2-22-220−2i2i−2i2i000002-22-200000000−2i2i00−2i2i00000000000000−i2i2−i2i2−i2i2−i2i2000000000000−22−22
χ3822-2-22-22-220002-22-202-2-2-22-220−2i2i−2i2i000002-22-200000000−2i2i00−2i2i00000000000000i2−i2i2−i2i2−i2i2−i20000000000002−22−2
χ392-222-2-22-222-2-2-2-2222-2-222-2-22-20000222-2-2-2-222000000-22000000000000000022-2-200000000000000-2200000000
χ402-222-2-22-222-2-2-2-2222-2-222-2-22-20000222-2-2-2-222000000-220000000000000000-2-222000000000000002-200000000
χ412-222-2-22-22-22222-2-2-2-2-222-2-22-22i2i−2i−2i2-2-22222-2-2−2i2i0000-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ422-222-2-22-22-22222-2-2-2-2-222-2-22-2−2i−2i2i2i2-2-22222-2-22i−2i0000-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ432-222-2-22-22-222-2-222-2-2-222-2-2220000-2-2-222-2-2220000002-20000000000000000000000000000000000002i−2i−2i2i0000
χ442-222-2-22-22-222-2-222-2-2-222-2-2220000-2-2-222-2-2220000002-2000000000000000000000000000000000000−2i2i2i−2i0000
χ452-222-2-22-2-12-2-222-2-2211-1-111-122i2i−2i−2i-2-1-111-1-1112i−2i2i2i−2i−2i-11−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-1110000000000
χ462-222-2-22-2-12-2-222-2-2211-1-111-122i2i−2i−2i-2-1-111-1-1112i−2i−2i−2i2i2i-11−i−i−i−iiiiiiiii−i−i−i−i000000000000-2211-1-10000000000
χ472-222-2-22-2-12-2-222-2-2211-1-111-12−2i−2i2i2i-2-1-111-1-111−2i2i2i2i−2i−2i-11iiii−i−i−i−i−i−i−i−iiiii000000000000-2211-1-10000000000
χ482-222-2-22-2-12-2-222-2-2211-1-111-12−2i−2i2i2i-2-1-111-1-111−2i2i−2i−2i2i2i-11iiii−i−i−i−iiiii−i−i−i−i0000000000002-2-1-1110000000000
χ492-222-2-22-2-1-22222-2-2-211-1-111-1-22i2i−2i−2i211-1-1-1-111−2i2i00001-1−i−iiiii−i−i33−3−3−3−33300000000000000−i3i3i3−i30000000000
χ502-222-2-22-2-1-22222-2-2-211-1-111-1-22i2i−2i−2i211-1-1-1-111−2i2i00001-1−i−iiiii−i−i−3−33333−3−300000000000000i3−i3−i3i30000000000
χ512-222-2-22-2-1-22222-2-2-211-1-111-1-2−2i−2i2i2i211-1-1-1-1112i−2i00001-1ii−i−i−i−iii33−3−3−3−33300000000000000i3−i3−i3i30000000000
χ522-222-2-22-2-1-22222-2-2-211-1-111-1-2−2i−2i2i2i211-1-1-1-1112i−2i00001-1ii−i−i−i−iii−3−33333−3−300000000000000−i3i3i3−i30000000000
χ532-22-222-2-22-2-2200002-2-22-222-20000002-2-22000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i22i−2i−2i2i−2−22222−2−20000000000000000
χ542-22-222-2-22-2-2200002-2-22-222-20000002-2-22000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2−2i2i2i−2i22−2−2−2−2220000000000000000
χ552-22-222-2-22-2-2200002-2-22-222-20000002-2-22000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i22i−2i−2i2i22−2−2−2−2220000000000000000
χ562-22-222-2-22-2-2200002-2-22-222-20000002-2-22000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2−2i2i2i−2i−2−22222−2−20000000000000000
χ572-2-2-2-222220002-2-220-22-2-2-22202-2-22000002-2-22000000002-200-22000000000000002−22−2−22−22000000000000−222−2
χ582-2-2-2-222220002-2-220-22-2-2-22202-2-22000002-2-22000000002-200-2200000000000000−22−222−22−20000000000002−2−22
χ592-2-2-2-222220002-2-220-22-2-2-2220-222-2000002-2-2200000000-22002-2000000000000002−22−2−22−220000000000002−2−22
χ602-2-2-2-222220002-2-220-22-2-2-2220-222-2000002-2-2200000000-22002-200000000000000−22−222−22−2000000000000−222−2
χ6144444444-2444-4-4-4-44-2-2-2-2-2-2-2-40000-4-2-2-2-222220000002200000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-240000422222222000000-2-200000000000000000000000000000000000000000000
χ63444-4-4-4-4444-440000-4444-4-4-4-4000000-44-4400000000000000000000000000000000000000000000000000000000
χ64444-4-4-4-44-24-440000-4-2-2-222220000002-22-200000000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ65444-4-4-4-44-24-440000-4-2-2-222220000002-22-200000000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ66444-4-4-4-44-2-44-400004-2-2-22222000000-22-2200000022−2222−220000000000−22−22−22−220000000000000000000000000000
χ67444-4-4-4-44-2-44-400004-2-2-22222000000-22-22000000−2222−222200000000002−22−22−22−20000000000000000000000000000
χ6844-44-44-4-44000000004-4-44-44-40000000000000000000000000000000000000000002-2-222-2-220000000000000000
χ6944-44-44-4-44000000004-4-44-44-4000000000000000000000000000000000000000000-222-2-222-20000000000000000
χ7044-4-44-44-44000-44-4404-4-4-44-440000000000-44-440000000000000000000000000000000000000000000000000000
χ7144-4-44-44-4-20004-44-40-2222-22-204i−4i4i−4i00000-22-2200000000−2i2i00−2i2i00000000000000000000000000000000000000
χ7244-4-44-44-4-20004-44-40-2222-22-20−4i4i−4i4i00000-22-22000000002i−2i002i−2i00000000000000000000000000000000000000
χ7344-4-44-44-4-2000-44-440-2222-22-200000000002-22-20000000000−2i32i300−2i32i3000000000000000000000000000000000000
χ7444-4-44-44-4-2000-44-440-2222-22-200000000002-22-200000000002i3−2i3002i3−2i3000000000000000000000000000000000000
χ754-444-4-44-4-24-4-4-4-444422-2-222-2-400004-2-22222-2-20000002-200000000000000000000000000000000000000000000
χ764-444-4-44-4-2-444-4-444-422-2-222-240000-422-2-222-2-2000000-2200000000000000000000000000000000000000000000
χ774-44-444-4-4444-40000-4-4-44-444-4000000-444-400000000000000000000000000000000000000000000000000000000
χ784-44-444-4-4-244-40000-422-22-2-220000002-2-22000000000000000000006−6−66−666−60000000000000000000000000000
χ794-44-444-4-4-244-40000-422-22-2-220000002-2-2200000000000000000000−666−66−6−660000000000000000000000000000
χ804-44-444-4-4-2-4-440000422-22-2-22000000-222-2000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i20000000000000000000000000000
χ814-44-444-4-4-2-4-440000422-22-2-22000000-222-20000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i20000000000000000000000000000
χ824-4-444-4-44400000000-44-444-4-40000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ834-4-444-4-44400000000-44-444-4-4000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ844-4-4-4-44444000-444-40-44-4-4-4440000000000-444-40000000000000000000000000000000000000000000000000000
χ854-4-4-4-4444-20004-4-4402-2222-2-204-4-4400000-222-200000000-22002-200000000000000000000000000000000000000
χ864-4-4-4-4444-20004-4-4402-2222-2-20-444-400000-222-2000000002-200-2200000000000000000000000000000000000000
χ874-4-4-4-4444-2000-444-402-2222-2-200000000002-2-22000000000023−2300−2323000000000000000000000000000000000000
χ884-4-4-4-4444-2000-444-402-2222-2-200000000002-2-220000000000−23230023−23000000000000000000000000000000000000
χ8988-88-88-8-8-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-8-88-4000000004-44-4-444000000000000000000000000000000000000000000000000000000000000000000

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