Finite Group Databasebeta

← Group #10690439

Character table — Group #10690439

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order122222223444444446666666444444121212121212121244888812121212121212121212242424242424242444448888888844121212122222448888
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
χ51111111111111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ61111111111111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ71111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111
χ81111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ91-111-11-1-1111-111-1-1-1-1-111-1-11-1ii−i−i111-111-1-1-1i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i1111-1-1-1-11-111-1-111-1-1i−iii−i−i
χ101-111-11-1-1111-111-1-1-1-1-111-1-11-1ii−i−i111-111-1-1-1i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1-1-111111-111-1-1-1-111−ii−i−iii
χ111-111-11-1-1111-111-1-1-1-1-111-1-11-1ii−i−i111-111-1-1-1i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i-1-1-1-11111-11-1-11111-1-1i−i−i−iii
χ121-111-11-1-1111-111-1-1-1-1-111-1-11-1ii−i−i111-111-1-1-1i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiii−i−iii1111-1-1-1-1-11-1-111-1-111−iiii−i−i
χ131-111-11-1-1111-111-1-1-1-1-111-1-11-1−i−iii111-111-1-1-1−iiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i1111-1-1-1-1-11-1-111-1-111i−i−i−iii
χ141-111-11-1-1111-111-1-1-1-1-111-1-11-1−i−iii111-111-1-1-1−iiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iii-1-1-1-11111-11-1-11111-1-1−iiii−i−i
χ151-111-11-1-1111-111-1-1-1-1-111-1-11-1−i−iii111-111-1-1-1−ii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1-1-111111-111-1-1-1-111i−iii−i−i
χ161-111-11-1-1111-111-1-1-1-1-111-1-11-1−i−iii111-111-1-1-1−ii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii1111-1-1-1-11-111-1-111-1-1−ii−i−iii
χ17222222222222-2-2-22-22222222-22222-2222-2-2-2-22-2-20000-2-222-2-222-2-2000000000000000000000000000000000000
χ18222222222222-2-2-22-22222222-2-2-2-2-2-2222-2-2-2-22220000-2-2-2-222-2-222000000000000000000000000000000000000
χ19222222222-2-2-2222-222222222-20000-2-2-2-22222-2000000-2-200000000000000002222000000000000000000-2-20000
χ20222222222-2-2-2222-222222222-20000-2-2-2-22222-2000000-2-20000000000000000-2-2-2-2000000000000000000220000
χ21222222222-2-2-2-2-2-2-2-22222222200002-2-2-2-2-2-2-2-20000002200000000000000000000000000000000002-22-2000000
χ22222222222-2-2-2-2-2-2-2-22222222200002-2-2-2-2-2-2-2-2000000220000000000000000000000000000000000-22-22000000
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
χ2722222222-1222-2-2-22-2-1-1-1-1-1-1-1-22222-2-1-1-11111-1-2-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ2822222222-1222-2-2-22-2-1-1-1-1-1-1-1-22222-2-1-1-11111-1-2-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ2922222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-12200001111-1-111-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ3022222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-12200001111-1-111-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ31222-22-2-2-222-2-2000202-22-22-2-202i−2i2i−2i02-2-200002000000002i−2i002i−2i00000000000000−i2−i2i2i2−i2−i2i2i20000000000002−22−2
χ32222-22-2-2-222-2-2000202-22-22-2-202i−2i2i−2i02-2-200002000000002i−2i002i−2i00000000000000i2i2−i2−i2i2i2−i2−i2000000000000−22−22
χ33222-22-2-2-222-2-2000202-22-22-2-20−2i2i−2i2i02-2-20000200000000−2i2i00−2i2i00000000000000−i2−i2i2i2−i2−i2i2i2000000000000−22−22
χ34222-22-2-2-222-2-2000202-22-22-2-20−2i2i−2i2i02-2-20000200000000−2i2i00−2i2i00000000000000i2i2−i2−i2i2i2−i2−i20000000000002−22−2
χ3522-2-2-222-220002-220-222-2-2-2-220000000002-22-2000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i22i−2i2i−2i2−22−22−22−20000000000000000
χ3622-2-2-222-220002-220-222-2-2-2-220000000002-22-2000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i−22−22−22−220000000000000000
χ3722-2-2-222-220002-220-222-2-2-2-220000000002-22-2000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i22i−2i2i−2i−22−22−22−220000000000000000
χ3822-2-2-222-220002-220-222-2-2-2-220000000002-22-2000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i2−22−22−22−20000000000000000
χ392-222-22-2-2222-2-2-22-22-2-222-2-2222i2i−2i−2i-222-2-2-222-2−2i2i0000-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ402-222-22-2-2222-2-2-22-22-2-222-2-222−2i−2i2i2i-222-2-2-222-22i−2i0000-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ412-222-22-2-22-2-2222-22-2-2-222-2-2220000-2-2-2222-2-22000000-2200000000000000002i2i−2i−2i000000000000000000−2i2i0000
χ422-222-22-2-22-2-2222-22-2-2-222-2-2220000-2-2-2222-2-22000000-220000000000000000−2i−2i2i2i0000000000000000002i−2i0000
χ432-222-22-2-22-2-22-2-2222-2-222-2-22-200002-2-22-2-22220000002-200000000000000000000000000000000002-2-22000000
χ442-222-22-2-22-2-22-2-2222-2-222-2-22-200002-2-22-2-22220000002-20000000000000000000000000000000000-222-2000000
χ452-222-22-2-2-122-222-2-2-211-1-111-1-22i2i−2i−2i2-1-11-1-11112i−2i2i2i−2i−2i-11−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-1110000000000
χ462-222-22-2-2-122-222-2-2-211-1-111-1-22i2i−2i−2i2-1-11-1-11112i−2i−2i−2i2i2i-11−i−i−i−iiiiiiiii−i−i−i−i000000000000-2211-1-10000000000
χ472-222-22-2-2-122-222-2-2-211-1-111-1-2−2i−2i2i2i2-1-11-1-1111−2i2i2i2i−2i−2i-11iiii−i−i−i−i−i−i−i−iiiii000000000000-2211-1-10000000000
χ482-222-22-2-2-122-222-2-2-211-1-111-1-2−2i−2i2i2i2-1-11-1-1111−2i2i−2i−2i2i2i-11iiii−i−i−i−iiiii−i−i−i−i0000000000002-2-1-1110000000000
χ492-222-22-2-2-122-2-2-22-2211-1-111-122i2i−2i−2i-2-1-1111-1-11−2i2i00001-1−i−iiiii−i−i33−3−3−3−33300000000000000−i3i3i3−i30000000000
χ502-222-22-2-2-122-2-2-22-2211-1-111-122i2i−2i−2i-2-1-1111-1-11−2i2i00001-1−i−iiiii−i−i−3−33333−3−300000000000000i3−i3−i3i30000000000
χ512-222-22-2-2-122-2-2-22-2211-1-111-12−2i−2i2i2i-2-1-1111-1-112i−2i00001-1ii−i−i−i−iii33−3−3−3−33300000000000000i3−i3−i3i30000000000
χ522-222-22-2-2-122-2-2-22-2211-1-111-12−2i−2i2i2i-2-1-1111-1-112i−2i00001-1ii−i−i−i−iii−3−33333−3−300000000000000−i3i3i3−i30000000000
χ532-22-2-2-22222-22000-20-222-2-22-202-2-2202-220000-2000000002-200-2200000000000000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2
χ542-22-2-2-22222-22000-20-222-2-22-202-2-2202-220000-2000000002-200-2200000000000000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2
χ552-22-2-2-22222-22000-20-222-2-22-20-222-202-220000-200000000-22002-200000000000000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2
χ562-22-2-2-22222-22000-20-222-2-22-20-222-202-220000-200000000-22002-200000000000000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2
χ572-2-2-222-2220002-2-202-2-2-2-22220000000002-2-220002−2−2200000000002−22−2−22−222-2-22−22−222−22−20000000000000000
χ582-2-2-222-2220002-2-202-2-2-2-22220000000002-2-220002−2−2200000000002−22−2−22−22-222-22−22−2−22−220000000000000000
χ592-2-2-222-2220002-2-202-2-2-2-22220000000002-2-22000−222−20000000000−22−222−22−22-2-222−22−2−22−220000000000000000
χ602-2-2-222-2220002-2-202-2-2-2-22220000000002-2-22000−222−20000000000−22−222−22−2-222-2−22−222−22−20000000000000000
χ6144444444-2-4-4-4444-44-2-2-2-2-2-2-2-40000-4222-2-2-2-220000002200000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-240000422222222000000-2-200000000000000000000000000000000000000000000
χ63444-44-4-4-44-444000-404-44-44-4-4000000-4440000-40000000000000000000000000000000000000000000000000000
χ64444-44-4-4-4-24-4-400040-22-22-22204i−4i4i−4i0-2220000-200000000−2i2i00−2i2i00000000000000000000000000000000000000
χ65444-44-4-4-4-24-4-400040-22-22-2220−4i4i−4i4i0-2220000-2000000002i−2i002i−2i00000000000000000000000000000000000000
χ66444-44-4-4-4-2-444000-40-22-22-2220000002-2-2000020000000000−2i32i300−2i32i3000000000000000000000000000000000000
χ67444-44-4-4-4-2-444000-40-22-22-2220000002-2-20000200000000002i3−2i3002i3−2i3000000000000000000000000000000000000
χ6844-44-4-4-444000000004-4-44-44-40000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ6944-44-4-4-444000000004-4-44-44-4000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ7044-4-4-444-44000-44-40444-4-4-4-44000000000-44-4400000000000000000000000000000000000000000000000000000
χ7144-4-4-444-4-20004-440-4-2-22222-2000000000-22-22000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ7244-4-4-444-4-20004-440-4-2-22222-2000000000-22-220002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ7344-4-4-444-4-2000-44-404-2-22222-20000000002-22-2000000000000000006−6−666−6−660000000000000000000000000000
χ7444-4-4-444-4-2000-44-404-2-22222-20000000002-22-200000000000000000−666−6−666−60000000000000000000000000000
χ754-444-44-4-4-2-4-4444-44-422-2-222-240000-422-2-2-222-20000002-200000000000000000000000000000000000000000000
χ764-444-44-4-4-2-4-44-4-444422-2-222-2-40000422-222-2-2-2000000-2200000000000000000000000000000000000000000000
χ774-44-4-4-4444-44-400040-444-4-44-4000000-44-4000040000000000000000000000000000000000000000000000000000
χ784-44-4-4-444-24-44000-402-2-222-2204-4-440-22-20000200000000-22002-200000000000000000000000000000000000000
χ794-44-4-4-444-24-44000-402-2-222-220-444-40-22-200002000000002-200-2200000000000000000000000000000000000000
χ804-44-4-4-444-2-44-4000402-2-222-220000002-220000-2000000000023−2300−2323000000000000000000000000000000000000
χ814-44-4-4-444-2-44-4000402-2-222-220000002-220000-20000000000−23230023−23000000000000000000000000000000000000
χ824-4-444-44-4400000000-44-444-4-40000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ834-4-444-44-4400000000-44-444-4-4000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ844-4-4-444-444000-4440-4-4-4-4-4444000000000-444-400000000000000000000000000000000000000000000000000000
χ854-4-4-444-44-20004-4-4042222-2-2-2000000000-222-200022−22−22220000000000−22−222−22−20000000000000000000000000000
χ864-4-4-444-44-20004-4-4042222-2-2-2000000000-222-2000−222222−2200000000002−22−2−22−220000000000000000000000000000
χ874-4-4-444-44-2000-4440-42222-2-2-20000000002-2-2200000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ884-4-4-444-44-2000-4440-42222-2-2-20000000002-2-2200000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ8988-88-8-8-88-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-88-8-4000000004-44-4-444000000000000000000000000000000000000000000000000000000000000000000

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