Finite Group Databasebeta

← Group #10690874

Character table — Group #10690874

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212888888881212242424242424242424242424242424242244444444121212128888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-111-1-1ii−i−iii−i−i1-1
χ10111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-1-1-111111-111-1-1−i−iii−i−iii-11
χ11111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii11iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-11-1-111ii−i−i−i−iii-11
χ12111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii11iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11-1-111−i−iiiii−i−i1-1
χ13111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i11−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-11-1-111−i−iiiii−i−i-11
χ14111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-11-1-111ii−i−i−i−iii1-1
χ15111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11-111-1-1−i−iii−i−iii1-1
χ16111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111111-111-1-1ii−i−iii−i−i-11
χ1722222222222-2-22-22-22222222-2-2222-2-2-22-200000000-2-2000000000000000022-2-222-2-20000000000000000
χ1822222222222-2-22-22-22222222-2-2222-2-2-22-200000000-2-20000000000000000-2-222-2-2220000000000000000
χ19222222222-2-222-22-222222222-2-2-2-2-2222-2200000000-2-2000000000000000022-2-2-2-2220000000000000000
χ20222222222-2-222-22-222222222-2-2-2-2-2222-2200000000-2-20000000000000000-2-22222-2-20000000000000000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ2522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122111111112i2i−2i−2i2i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii000000002-2-1-1110000000000
χ2622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122111111112i2i−2i−2i−2i−2i2i2i-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000-2211-1-10000000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111−2i−2i2i2i2i2i−2i−2i-1-1iiii−i−i−i−i−i−i−i−iiiii00000000-2211-1-10000000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111−2i−2i2i2i−2i−2i2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i000000002-2-1-1110000000000
χ2922-2-22-2-2222-20020-2022-2-22-2-2002-2-2000200000−i2i2−i2i20000000000−i2−i2i2i2−i2−i2i2i2002i−2i002i−2i00000000002−22−200
χ3022-2-22-2-2222-20020-2022-2-22-2-2002-2-2000200000−i2i2−i2i20000000000−i2−i2i2i2−i2−i2i2i200−2i2i00−2i2i0000000000−22−2200
χ3122-2-22-2-2222-20020-2022-2-22-2-2002-2-2000200000i2−i2i2−i20000000000i2i2−i2−i2i2i2−i2−i2002i−2i002i−2i0000000000−22−2200
χ3222-2-22-2-2222-20020-2022-2-22-2-2002-2-2000200000i2−i2i2−i20000000000i2i2−i2−i2i2i2−i2−i200−2i2i00−2i2i00000000002−22−200
χ3322-2-22-2-222-2200-202022-2-22-2-200-222000-2000002−2−22000000000022−2−2−2−222002i−2i00−2i2i0000000000i2−i2−i2i200
χ3422-2-22-2-222-2200-202022-2-22-2-200-222000-2000002−2−22000000000022−2−2−2−22200−2i2i002i−2i0000000000−i2i2i2−i200
χ3522-2-22-2-222-2200-202022-2-22-2-200-222000-200000−222−20000000000−2−22222−2−2002i−2i00−2i2i0000000000−i2i2i2−i200
χ3622-2-22-2-222-2200-202022-2-22-2-200-222000-200000−222−20000000000−2−22222−2−200−2i2i002i−2i0000000000i2−i2−i2i200
χ372-2-2-2222-22222-2-22-2-2-2-2-2-22222-222-22-2-2-22000000002-20000000000000000000000000000002i−2i2i−2i000000
χ382-2-2-2222-22222-2-22-2-2-2-2-2-22222-222-22-2-2-22000000002-2000000000000000000000000000000−2i2i−2i2i000000
χ392-2-2-2222-2222-22-2-2-22-2-2-2-2222-2222-2-222-2-22i−2i2i−2i0000-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ402-2-2-2222-2222-22-2-2-22-2-2-2-2222-2222-2-222-2-2−2i2i−2i2i0000-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ412-2-2-2222-22-2-22-2222-2-2-2-2-2222-22-2-222-2-2222-2-220000-2222-2-2-2-22200000000000000000000000000000000
χ422-2-2-2222-22-2-22-2222-2-2-2-2-2222-22-2-222-2-222-222-20000-22-2-22222-2-200000000000000000000000000000000
χ432-2-2-2222-22-2-2-222-222-2-2-2-22222-2-2-22-2222-2000000002-20000000000000000000000000000002-2-22000000
χ442-2-2-2222-22-2-2-222-222-2-2-2-22222-2-2-22-2222-2000000002-2000000000000000000000000000000-222-2000000
χ452-2-2-2222-2-122-22-2-2-221111-1-1-1-22-1-111-1-1112i−2i2i−2i00001-1−i−iii−i−iii3−33−33−33−30000000000−i3i3−i3i30000000000
χ462-2-2-2222-2-122-22-2-2-221111-1-1-1-22-1-111-1-1112i−2i2i−2i00001-1−i−iii−i−iii−33−33−33−330000000000i3−i3i3−i30000000000
χ472-2-2-2222-2-122-22-2-2-221111-1-1-1-22-1-111-1-111−2i2i−2i2i00001-1ii−i−iii−i−i3−33−33−33−30000000000i3−i3i3−i30000000000
χ482-2-2-2222-2-122-22-2-2-221111-1-1-1-22-1-111-1-111−2i2i−2i2i00001-1ii−i−iii−i−i−33−33−33−330000000000−i3i3−i3i30000000000
χ492-2-2-2222-2-1-2-22-2222-21111-1-1-1-2211-1-111-1-12-2-2200001-1-1-11111-1-1−i3i3−i3i3i3−i3i3−i30000000000−i3i3i3−i30000000000
χ502-2-2-2222-2-1-2-22-2222-21111-1-1-1-2211-1-111-1-12-2-2200001-1-1-11111-1-1i3−i3i3−i3−i3i3−i3i30000000000i3−i3−i3i30000000000
χ512-2-2-2222-2-1-2-22-2222-21111-1-1-1-2211-1-111-1-1-222-200001-111-1-1-1-111−i3i3−i3i3i3−i3i3−i30000000000i3−i3−i3i30000000000
χ522-2-2-2222-2-1-2-22-2222-21111-1-1-1-2211-1-111-1-1-222-200001-111-1-1-1-111i3−i3i3−i3−i3i3−i3i30000000000−i3i3i3−i30000000000
χ5344444444-244-4-44-44-4-2-2-2-2-2-2-2-4-4-2-2-2222-2200000000220000000000000000000000000000000000000000
χ5444444444-2-4-444-44-44-2-2-2-2-2-2-2-4-4222-2-2-22-200000000220000000000000000000000000000000000000000
χ55444-4-44-4-44000000004-44-4-44-40000000000000000000000000000000000004-40000000000000000000000
χ56444-4-44-4-44000000004-44-4-44-4000000000000000000000000000000000000-440000000000000000000000
χ5744-44-4-44-4400440-40-44-4-44-4-440000044-40-400000000000000000000000000000000000000000000000000
χ5844-44-4-44-4400-4-404044-4-44-4-4400000-4-440400000000000000000000000000000000000000000000000000
χ5944-44-4-44-4-200440-40-4-222-222-200000-2-220200000000006−66−66−66−600000000000000000000000000000000
χ6044-44-4-44-4-200440-40-4-222-222-200000-2-22020000000000−66−66−66−6600000000000000000000000000000000
χ6144-44-4-44-4-200-4-40404-222-222-20000022-20-20000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ6244-44-4-44-4-200-4-40404-222-222-20000022-20-20000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ6344-4-44-4-44-24-40040-40-2-222-22200-222000-200000−2i22i2−2i22i20000000000i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ6444-4-44-4-44-24-40040-40-2-222-22200-222000-2000002i2−2i22i2−2i20000000000−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ6544-4-44-4-44-2-4400-4040-2-222-222002-2-200020000022−22−22220000000000−2−22222−2−2000000000000000000000000
χ6644-4-44-4-44-2-4400-4040-2-222-222002-2-2000200000−222222−22000000000022−2−2−2−222000000000000000000000000
χ674-4444-4-4-444-400-4040-4-4444-4-4004-44000-4000000000000000000000000000000000000000000000000000
χ684-4444-4-4-44-440040-40-4-4444-4-400-44-40004000000000000000000000000000000000000000000000000000
χ694-4444-4-4-4-24-400-404022-2-2-22200-22-200020000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ704-4444-4-4-4-24-400-404022-2-2-22200-22-200020000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ714-4444-4-4-4-2-440040-4022-2-2-222002-22000-200000000000000000006−6−66−666−6000000000000000000000000
χ724-4444-4-4-4-2-440040-4022-2-2-222002-22000-20000000000000000000−666−66−6−66000000000000000000000000
χ734-44-4-4-4444004-40-404-444-4-4-44000004-440-400000000000000000000000000000000000000000000000000
χ744-44-4-4-444400-44040-4-444-4-4-4400000-44-40400000000000000000000000000000000000000000000000000
χ754-44-4-4-444-2004-40-4042-2-2222-200000-22-20200000000006−6−66−666−600000000000000000000000000000000
χ764-44-4-4-444-2004-40-4042-2-2222-200000-22-2020000000000−666−66−6−6600000000000000000000000000000000
χ774-44-4-4-444-200-44040-42-2-2222-2000002-220-20000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000
χ784-44-4-4-444-200-44040-42-2-2222-2000002-220-20000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000
χ794-4-44-44-44400000000-44-44-44-400000000000000000000000000000000000000004i−4i000000000000000000
χ804-4-44-44-44400000000-44-44-44-40000000000000000000000000000000000000000−4i4i000000000000000000
χ814-4-4-4444-4-2444-4-44-4-42222-2-2-24-4-2-22-2222-200000000-220000000000000000000000000000000000000000
χ824-4-4-4444-4-2-4-4-444-4442222-2-2-24-422-22-2-2-2200000000-220000000000000000000000000000000000000000
χ83888-8-88-8-8-400000000-44-444-44000000000000000000000000000000000000000000000000000000000000
χ848-8-88-88-88-4000000004-44-44-44000000000000000000000000000000000000000000000000000000000000

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