Finite Group Databasebeta

← Group #10691422

Character table — Group #10691422

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order12222222344444444666666644121212121212121222446666888812121212121224242424242424248888888844121212128888888822
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91-1-1-1111-111-111-1-11-1-1-1-1111-11-111-111-1-1-11-11-111-1-1ii−i−i1-111-1-1iiii−i−i−i−iii−i−iii−i−ii−iii−i−i11-1-1ii−i−i1-1
χ101-1-1-1111-111-111-1-11-1-1-1-1111-11-111-111-1-1-11-11-111-1-1ii−i−i1-111-1-1iiii−i−i−i−i−i−iii−i−iiii−iii−i−i-1-111−i−iii-11
χ111-1-1-1111-111-111-1-11-1-1-1-1111-11-111-111-1-1-11-11-111-1-1−i−iii1-111-1-1−i−i−i−iiiiiii−i−iii−i−i−ii−i−iii-1-111ii−i−i-11
χ121-1-1-1111-111-111-1-11-1-1-1-1111-11-111-111-1-1-11-11-111-1-1−i−iii1-111-1-1−i−i−i−iiiii−i−iii−i−iii−ii−i−iii11-1-1−i−iii1-1
χ131-1-1-1111-111-111-1-11-1-1-1-1111-11-111-111-1-1-1-11-11-1-111ii−i−i1-1-1-111iiii−i−i−i−iii−i−iii−i−i−ii−i−iii11-1-1−i−iii-11
χ141-1-1-1111-111-111-1-11-1-1-1-1111-11-111-111-1-1-1-11-11-1-111ii−i−i1-1-1-111iiii−i−i−i−i−i−iii−i−iii−ii−i−iii-1-111ii−i−i1-1
χ151-1-1-1111-111-111-1-11-1-1-1-1111-11-111-111-1-1-1-11-11-1-111−i−iii1-1-1-111−i−i−i−iiiiiii−i−iii−i−ii−iii−i−i-1-111−i−iii1-1
χ161-1-1-1111-111-111-1-11-1-1-1-1111-11-111-111-1-1-1-11-11-1-111−i−iii1-1-1-111−i−i−i−iiiii−i−iii−i−iiii−iii−i−i11-1-1ii−i−i-11
χ1722222222222-2-22-22-22222222-2-2222-2-2-2-2222-2-222220000-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222-2-22-22-22222222-2-2222-2-2-2-22-2-222-2-2-2-20000-2-2222200000000000000000000000000000000
χ19222222222-2-222-22-222222222-2-2-2-2-22222-2000000000000-2-20000000000002222-2-2-2-20000000000000000
χ20222222222-2-222-22-222222222-2-2-2-2-22222-2000000000000-2-2000000000000-2-2-2-222220000000000000000
χ21222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000220000000000000000000000000000002i−2i2i−2i00
χ22222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000000022000000000000000000000000000000−2i2i−2i2i00
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-11111111100000000-2-211110000000000
χ2522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-11111111111110000000022-1-1-1-10000000000
χ2722222222-122-2-22-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2-1-1-1-10000111111−i3−i3i3i3−i3−i3i3i30000000000−i3i3−i3i30000000000
χ2822222222-122-2-22-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2-1-1-1-10000111111i3i3−i3−i3i3i3−i3−i30000000000i3−i3i3−i30000000000
χ2922222222-122-2-22-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2221111000011-1-1-1-1−i3−i3i3i3−i3−i3i3i30000000000i3−i3i3−i30000000000
χ3022222222-122-2-22-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2221111000011-1-1-1-1i3i3−i3−i3i3i3−i3−i30000000000−i3i3−i3i30000000000
χ31222-2-2-22-22002-2020-222-2-2-22-2000002-22-2000000000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i200002i−2i2i−2i0000002−22−2000000
χ32222-2-2-22-22002-2020-222-2-2-22-2000002-22-2000000000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i20000−2i2i−2i2i000000−22−22000000
χ33222-2-2-22-22002-2020-222-2-2-22-2000002-22-2000000000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i200002i−2i2i−2i000000−22−22000000
χ34222-2-2-22-22002-2020-222-2-2-22-2000002-22-2000000000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i20000−2i2i−2i2i0000002−22−2000000
χ352-2-22-2-2222002-20-202-2-22-2-222000002-2-220000000002−2−220000002−22−2−22−2200002-2-22000000−222−2000000
χ362-2-22-2-2222002-20-202-2-22-2-222000002-2-220000000002−2−220000002−22−2−22−220000-222-20000002−2−22000000
χ372-2-22-2-2222002-20-202-2-22-2-222000002-2-22000000000−222−2000000−22−222−22−200002-2-220000002−2−22000000
χ382-2-22-2-2222002-20-202-2-22-2-222000002-2-22000000000−222−2000000−22−222−22−20000-222-2000000−222−2000000
χ392-2-2-2222-222-2-2-2-2222-2-2-2222-2-2222-2-2-222-22-2-2222-2-20000-22-2-22200000000000000000000000000000000
χ402-2-2-2222-222-2-2-2-2222-2-2-2222-2-2222-2-2-222-2-222-2-2-2220000-2222-2-200000000000000000000000000000000
χ412-2-2-2222-22-22222-2-2-2-2-2-2222-2-22-2-2222-2-22000000000000-220000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ422-2-2-2222-22-22222-2-2-2-2-2-2222-2-22-2-2222-2-22000000000000-22000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ432-2-2-2222-22-22-2-222-22-2-2-2222-22-2-2-22-2-22220000000000002-20000000000000000000000000000002-2-2200
χ442-2-2-2222-22-22-2-222-22-2-2-2222-22-2-2-22-2-22220000000000002-2000000000000000000000000000000-222-200
χ452-2-2-2222-2-12-222-2-22-2111-1-1-112-2-1-11-1-11112-22-2-1-1112i2i−2i−2i-11-1-111−i−i−i−iiiii000000002i−2i−i−iii0000000000
χ462-2-2-2222-2-12-222-2-22-2111-1-1-112-2-1-11-1-11112-22-2-1-111−2i−2i2i2i-11-1-111iiii−i−i−i−i00000000−2i2iii−i−i0000000000
χ472-2-2-2222-2-12-222-2-22-2111-1-1-112-2-1-11-1-1111-22-2211-1-12i2i−2i−2i-1111-1-1−i−i−i−iiiii00000000−2i2iii−i−i0000000000
χ482-2-2-2222-2-12-222-2-22-2111-1-1-112-2-1-11-1-1111-22-2211-1-1−2i−2i2i2i-1111-1-1iiii−i−i−i−i000000002i−2i−i−iii0000000000
χ492-2-2-2222-2-12-2-2-2-2222111-1-1-11-22-1-1111-1-112-2-22-1-11100001-111-1-133−3−3−3−33300000000003−3−330000000000
χ502-2-2-2222-2-12-2-2-2-2222111-1-1-11-22-1-1111-1-112-2-22-1-11100001-111-1-1−3−33333−3−30000000000−333−30000000000
χ512-2-2-2222-2-12-2-2-2-2222111-1-1-11-22-1-1111-1-11-222-211-1-100001-1-1-11133−3−3−3−3330000000000−333−30000000000
χ522-2-2-2222-2-12-2-2-2-2222111-1-1-11-22-1-1111-1-11-222-211-1-100001-1-1-111−3−33333−3−300000000003−3−330000000000
χ5344444444-2-4-444-44-44-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000000022000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222000000000000-2-2000000000000000000000000000000000000
χ55444-4-4-44-4400-440-40444-4-4-44-400000-44-44000000000000000000000000000000000000000000000000000
χ56444-4-4-44-4-2004-4040-4-2-2222-2200000-22-22000000000−2i22i2−2i22i2000000i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ57444-4-4-44-4-2004-4040-4-2-2222-2200000-22-220000000002i2−2i22i2−2i2000000−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ58444-4-4-44-4-200-440-404-2-2222-22000002-22-200000000000000000006−6−666−6−66000000000000000000000000
χ59444-4-4-44-4-200-440-404-2-2222-22000002-22-20000000000000000000−666−6−666−6000000000000000000000000
χ6044-444-4-4-44000000004-444-4-4-4000000000000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ6144-444-4-4-44000000004-444-4-4-40000000000000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ6244-4-4-44-4444-40040-404-4-4-44-44004-4-40000400000000000000000000000000000000000000000000000000
χ6344-4-4-44-444-4400-40404-4-4-44-4400-4440000-400000000000000000000000000000000000000000000000000
χ6444-4-4-44-44-24-40040-40-2222-22-200-2220000-20000−2i32i3−2i32i3000000000000000000000000000000000000000000
χ6544-4-4-44-44-24-40040-40-2222-22-200-2220000-200002i3−2i32i3−2i3000000000000000000000000000000000000000000
χ6644-4-4-44-44-2-4400-4040-2222-22-2002-2-2000020000000000000023−2323−2300000000000000000000000000000000
χ6744-4-4-44-44-2-4400-4040-2222-22-2002-2-20000200000000000000−2323−232300000000000000000000000000000000
χ684-444-44-4-444400-40-40-444-44-4-4004-440000-400000000000000000000000000000000000000000000000000
χ694-444-44-4-44-4-4004040-444-44-4-400-44-40000400000000000000000000000000000000000000000000000000
χ704-444-44-4-4-24400-40-402-2-22-22200-22-2000020000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ714-444-44-4-4-24400-40-402-2-22-22200-22-20000200002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ724-444-44-4-4-2-4-40040402-2-22-222002-220000-20000000000000023−23−232300000000000000000000000000000000
χ734-444-44-4-4-2-4-40040402-2-22-222002-220000-200000000000000−232323−2300000000000000000000000000000000
χ744-44-44-4-44400000000-44-44-4-4400000000000000000000000000000000000022−22−222200000000000000000000
χ754-44-44-4-44400000000-44-44-4-44000000000000000000000000000000000000−222222−2200000000000000000000
χ764-4-44-4-444400-44040-4-4-44-4-44400000-444-4000000000000000000000000000000000000000000000000000
χ774-4-44-4-444-2004-40-40422-222-2-200000-222-200000000022−22−2222000000−22−222−22−2000000000000000000000000
χ784-4-44-4-444-2004-40-40422-222-2-200000-222-2000000000−222222−220000002−22−2−22−22000000000000000000000000
χ794-4-44-4-444-200-44040-422-222-2-2000002-2-220000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ804-4-44-4-444-200-44040-422-222-2-2000002-2-220000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ814-4-4-4444-4-2-44444-4-4-4222-2-2-22-4422-2-2-222-20000000000002-2000000000000000000000000000000000000
χ824-4-4-4444-4-2-44-4-444-44222-2-2-224-422-222-2-2-2000000000000-22000000000000000000000000000000000000
χ8388-888-8-8-8-400000000-44-4-4444000000000000000000000000000000000000000000000000000000000000
χ848-88-88-8-88-4000000004-44-444-4000000000000000000000000000000000000000000000000000000000000

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