Finite Group Databasebeta

← Group #10691056

Character table — Group #10691056

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212121212121616161616161616161624242424242424244848
order12222234444446664446612121212121212128888888812122424242424242424444488884412121212242424242488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ511111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ611111111111111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1
χ91111-1-111-1-11-1-111111-1-1-111-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−i11-1-1ii−i−i1-111-1-1ii−i−i-11i−iii−i−i1-1
χ101111-1-111-1-11-1-111111-1-1-111-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−i-1-111−i−iii1-111-1-1ii−i−i1-1−ii−i−iii-11
χ111111-1-111-1-11-1-111111-1-1-111-1-1-1-1-1-1ii−i−i−i−iii11−i−i−i−iiiii11-1-1ii−i−i-11-1-111ii−i−i-11i−i−i−iii-11
χ121111-1-111-1-11-1-111111-1-1-111-1-1-1-1-1-1ii−i−i−i−iii11−i−i−i−iiiii-1-111−i−iii-11-1-111ii−i−i1-1−iiii−i−i1-1
χ131111-1-111-1-11-1-111111-1-1-111-1-1-1-1-1-1−i−iiiii−i−i11iiii−i−i−i−i11-1-1−i−iii-11-1-111−i−iii-11−iiii−i−i-11
χ141111-1-111-1-11-1-111111-1-1-111-1-1-1-1-1-1−i−iiiii−i−i11iiii−i−i−i−i-1-111ii−i−i-11-1-111−i−iii1-1i−i−i−iii1-1
χ151111-1-111-1-11-1-111111-1-1-111-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii11-1-1−i−iii1-111-1-1−i−iii-11−ii−i−iii1-1
χ161111-1-111-1-11-1-111111-1-1-111-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii-1-111ii−i−i1-111-1-1−i−iii1-1i−iii−i−i-11
χ1722222222-2222-2222-2-2-222222-2-2-2-2200000000-2-200000000222200000000000000-2-200000000
χ1822222222-2222-2222-2-2-222222-2-2-2-2200000000-2-200000000-2-2-2-2000000000000002200000000
χ192222222-22-2-2-222222-2-222-2-2-222-2-2-22i−2i2i−2i00002-200000000000000000000002i−2i2i−2i0000000000
χ202222222-22-2-2-222222-2-222-2-2-222-2-2-2−2i2i−2i2i00002-20000000000000000000000−2i2i−2i2i0000000000
χ212222222-2-2-2-2-2-2222-22222-2-2-2-2-222-200000000-220000000000002i2i−2i−2i000000000000−2i2i000000
χ222222222-2-2-2-2-2-2222-22222-2-2-2-2-222-200000000-22000000000000−2i−2i2i2i0000000000002i−2i000000
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-10000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-11111111100000000-2-21111-1-1-1-10000000000
χ25222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100000000-2-2111111110000000000
χ26222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000000022-1-1-1-111110000000000
χ27222222-1-22-2-2-22-1-1-12-2-2-1-1111-1-11112i−2i2i−2i0000-1133−3−333−3−30000000000−i3i3−i3i3−ii−ii0000000000
χ28222222-1-22-2-2-22-1-1-12-2-2-1-1111-1-11112i−2i2i−2i0000-11−3−333−3−3330000000000i3−i3i3−i3−ii−ii0000000000
χ29222222-1-22-2-2-22-1-1-12-2-2-1-1111-1-1111−2i2i−2i2i0000-1133−3−333−3−30000000000i3−i3i3−i3i−ii−i0000000000
χ30222222-1-22-2-2-22-1-1-12-2-2-1-1111-1-1111−2i2i−2i2i0000-11−3−333−3−3330000000000−i3i3−i3i3i−ii−i0000000000
χ312222-2-2222-22-22222-2-22-2-222-22222-200000000-2-20000000022-2-2000000000000002-200000000
χ322222-2-2222-22-22222-2-22-2-222-22222-200000000-2-200000000-2-22200000000000000-2200000000
χ332222-2-22-222-222222-22-2-2-2-2-2222-2-2200000000-220000000000002222000000000000-2-2000000
χ342222-2-22-222-222222-22-2-2-2-2-2222-2-2200000000-22000000000000-2-2-2-200000000000022000000
χ352222-2-22-2-22-22-22222-22-2-2-2-22-2-22222-2-2200002-200000000000000000000002-2-220000000000
χ362222-2-22-2-22-22-22222-22-2-2-2-22-2-2222-222-200002-20000000000000000000000-222-20000000000
χ372222-2-2-12-2-22-2-2-1-1-122-211-1-11111112i2i−2i−2i2i2i−2i−2i-1-1−i−i−i−iiiii000000002-2-1-111−i−iii0000000000
χ382222-2-2-12-2-22-2-2-1-1-122-211-1-11111112i2i−2i−2i−2i−2i2i2i-1-1iiii−i−i−i−i00000000-2211-1-1−i−iii0000000000
χ392222-2-2-12-2-22-2-2-1-1-122-211-1-1111111−2i−2i2i2i2i2i−2i−2i-1-1−i−i−i−iiiii00000000-2211-1-1ii−i−i0000000000
χ402222-2-2-12-2-22-2-2-1-1-122-211-1-1111111−2i−2i2i2i−2i−2i2i2i-1-1iiii−i−i−i−i000000002-2-1-111ii−i−i0000000000
χ412222-2-2-1-2-22-22-2-1-1-12-221111-111-1-1-12-2-220000-11−i3−i3i3i3i3i3−i3−i30000000000−i3i3i3−i3-111-10000000000
χ422222-2-2-1-2-22-22-2-1-1-12-221111-111-1-1-12-2-220000-11i3i3−i3−i3−i3−i3i3i30000000000i3−i3−i3i3-111-10000000000
χ432222-2-2-1-2-22-22-2-1-1-12-221111-111-1-1-1-222-20000-11−i3−i3i3i3i3i3−i3−i30000000000i3−i3−i3i31-1-110000000000
χ442222-2-2-1-2-22-22-2-1-1-12-221111-111-1-1-1-222-20000-11i3i3−i3−i3−i3−i3i3i30000000000−i3i3i3−i31-1-110000000000
χ4522-2-22-22-2022-202-2-20002-22-2-2000020000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i22i−2i2i−2i0000000000000000002−22−200
χ4622-2-22-22-2022-202-2-20002-22-2-2000020000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i000000000000000000−22−2200
χ4722-2-22-22-2022-202-2-20002-22-2-2000020000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i22i−2i2i−2i000000000000000000−22−2200
χ4822-2-22-22-2022-202-2-20002-22-2-2000020000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i0000000000000000002−22−200
χ4922-2-2-222-20-22202-2-2000-222-220000-200002−2−22002−22−2−22−222i−2i−2i2i000000000000000000i2−i2−i2i200
χ5022-2-2-222-20-22202-2-2000-222-220000-200002−2−22002−22−2−22−22−2i2i2i−2i000000000000000000−i2i2i2−i200
χ5122-2-2-222-20-22202-2-2000-222-220000-20000−222−200−22−222−22−22i−2i−2i2i000000000000000000−i2i2i2−i200
χ5222-2-2-222-20-22202-2-2000-222-220000-20000−222−200−22−222−22−2−2i2i2i−2i000000000000000000i2−i2−i2i200
χ53444444-24-4444-4-2-2-2-4-4-4-2-2-2-2-22222-20000000022000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-2-444-2-222222-2-22000000002-2000000000000000000000000000000000000
χ554444-4-4-244-44-44-2-2-2-4-4422-2-22-2-2-2-220000000022000000000000000000000000000000000000
χ564444-4-4-2-444-444-2-2-2-44-42222-2-2-222-2000000002-2000000000000000000000000000000000000
χ5744-4-44-4440-4-4404-4-40004-4-4440000-40000000000000000000000000000000000000000000000
χ5844-4-44-4-240-4-440-222000-222-2-2000020000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ5944-4-44-4-240-4-440-222000-222-2-2000020000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ6044-4-44-4-2-4044-40-222000-22-2220000-20000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ6144-4-44-4-2-4044-40-222000-22-2220000-200002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ6244-4-4-444404-4-404-4-4000-44-44-4000040000000000000000000000000000000000000000000000
χ6344-4-4-44-2404-4-40-2220002-22-220000-200000000006−6−66−666−60000000000000000000000000000
χ6444-4-4-44-2404-4-40-2220002-22-220000-20000000000−666−66−6−660000000000000000000000000000
χ6544-4-4-44-2-40-4440-2220002-2-22-200002000022−22−222200−22−222−22−20000000000000000000000000000
χ6644-4-4-44-2-40-4440-2220002-2-22-2000020000−222222−22002−22−2−22−220000000000000000000000000000
χ674-44-400404000-4-44-4000000004-4000000000000000000000000022−2222−2200000000000000000000
χ684-44-400404000-4-44-4000000004-40000000000000000000000000−2222−222200000000000000000000
χ694-44-40040-40004-44-400000000-440000000000000000000000000−2i22i22i2−2i200000000000000000000
χ704-44-40040-40004-44-400000000-4400000000000000000000000002i2−2i2−2i22i200000000000000000000
χ718-88-800-408000-84-4400000000-440000000000000000000000000000000000000000000000000
χ728-88-800-40-800084-44000000004-40000000000000000000000000000000000000000000000000
χ738-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000
χ748-8-8800-400000044-40000000000−4i34i300000000000000000000000000000000000000000000000
χ758-8-8800-400000044-400000000004i3−4i300000000000000000000000000000000000000000000000

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