Finite Group Databasebeta

← Group #10690445

Character table — Group #10690445

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444444444444444444444448888121212121212121216161616161616161616242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444444444444441212121212121212444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1
χ91-111-1-11-1111-111-1-1-1-1-1-1-1111-111111-1-1-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i1-111-1-111-1-1i−ii−iii−i−iii−i−i
χ101-111-1-11-1111-111-1-1-1-1-1-1-1111-111111-1-1-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii1-111-1-111-1-1−ii−ii−i−iii−i−iii
χ111-111-1-11-1111-111-1-1-1-1-1-1-1111-111111-1-1-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-11-1-111-1-111−iii−iii−i−i−i−iii
χ121-111-1-11-1111-111-1-1-1-1-1-1-1111-111111-1-1-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-11-1-111-1-111i−i−ii−i−iiiii−i−i
χ131-111-1-11-1111-111-1-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1ii−i−iii−i−i-1111-1-1-1-111i−ii−i−i−iii−i−iii
χ141-111-1-11-1111-111-1-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1−i−iii−i−iii-1111-1-1-1-111−ii−iiii−i−iii−i−i
χ151-111-1-11-1111-111-1-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-111ii−i−i−i−iii1-1-1-11111-1-1−iii−i−i−iiiii−i−i
χ161-111-1-11-1111-111-1-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-111−i−iiiii−i−i1-1-1-11111-1-1i−i−iiii−i−i−i−iii
χ17222222222222-2-2-22-22222222-2-2000000002222-2-2-2-2-2-2-2-20000000000000000000022220000000000000000-2-200000000
χ18222222222222-2-2-22-22222222-2-2000000002222-2-2-2-2-2-2-2-200000000000000000000-2-2-2-200000000000000002200000000
χ19222222222-2-2-2222-222222222-2-200000000-2-2-2-2-2-22222-2-200000000000000000000000022220000000000-2-20000000000
χ20222222222-2-2-2222-222222222-2-200000000-2-2-2-2-2-22222-2-2000000000000000000000000-2-2-2-20000000000220000000000
χ21222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-222-2-2-2-22200000000000000002-22-200000000002-22-20000000000000000
χ22222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-222-2-2-2-2220000000000000000-22-220000000000-22-220000000000000000
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000022-1-1-1-1-1-1-1-1000000000000
χ2422222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211111111000000000000
χ2522222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111222200000000-2-2-1-1-1-11111000000000000
χ2622222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-200000000221111-1-1-1-1000000000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122000000001111-1-11111-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i32-22-20000000000-11-11−i3i3−i3i3000000000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122000000001111-1-11111-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-22-2200000000001-11-1i3−i3i3−i3000000000000
χ2922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122000000001111-1-11111-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i32-22-20000000000-11-11i3−i3i3−i3000000000000
χ3022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122000000001111-1-11111-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-22-2200000000001-11-1−i3i3−i3i3000000000000
χ31222-22-2-2-222-22000-2022-2-22-2-20022−2−222−2−22-22-20000000022−2−222−2−222−2−222−2−200002-22-20000000000000000002−22−20000
χ32222-22-2-2-222-22000-2022-2-22-2-20022−2−222−2−22-22-20000000022−2−222−2−222−2−222−2−20000-22-22000000000000000000−22−220000
χ33222-22-2-2-222-22000-2022-2-22-2-200−2−222−2−2222-22-200000000−2−222−2−222−2−222−2−22200002-22-2000000000000000000−22−220000
χ34222-22-2-2-222-22000-2022-2-22-2-200−2−222−2−2222-22-200000000−2−222−2−222−2−222−2−2220000-22-220000000000000000002−22−20000
χ3522-2-2-222-220002-220-22-22-2-2-22002−22−22−22−20000002-22-2002−22−22−22−22−22−22−22−2000000002i−2i2i−2i000000000000000000−i2i2−i2i2
χ3622-2-2-222-220002-220-22-22-2-2-22002−22−22−22−20000002-22-2002−22−22−22−22−22−22−22−200000000−2i2i−2i2i000000000000000000i2−i2i2−i2
χ3722-2-2-222-220002-220-22-22-2-2-2200−22−22−22−220000002-22-200−22−22−22−22−22−22−22−22000000002i−2i2i−2i000000000000000000i2−i2i2−i2
χ3822-2-2-222-220002-220-22-22-2-2-2200−22−22−22−220000002-22-200−22−22−22−22−22−22−22−2200000000−2i2i−2i2i000000000000000000−i2i2−i2i2
χ392-222-2-22-2222-2-2-22-22-2-2-2-22222-20000000022-2-222-2-222-2-2000000000000000000002i2i−2i−2i0000000000000000−2i2i00000000
χ402-222-2-22-2222-2-2-22-22-2-2-2-22222-20000000022-2-222-2-222-2-200000000000000000000−2i−2i2i2i00000000000000002i−2i00000000
χ412-222-2-22-22-2-2222-22-2-2-2-2-22222-200000000-2-2222222-2-2-2-20000000000000000000000002i2i−2i−2i0000000000−2i2i0000000000
χ422-222-2-22-22-2-2222-22-2-2-2-2-22222-200000000-2-2222222-2-2-2-2000000000000000000000000−2i−2i2i2i00000000002i−2i0000000000
χ432-222-2-22-22-2-22-2-2222-2-2-2-2222-2200000000-2-222-2-2-2-2222200000000000000002-2-2200000000002-2-220000000000000000
χ442-222-2-22-22-2-22-2-2222-2-2-2-2222-2200000000-2-222-2-2-2-222220000000000000000-222-20000000000-222-20000000000000000
χ452-222-2-22-2-122-222-2-2-21111-1-1-1-222222-2-2-2-2-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111111122-2-2000000002-2-1-111-1-111000000000000
χ462-222-2-22-2-122-222-2-2-21111-1-1-1-222222-2-2-2-2-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-2-22200000000-2211-1-111-1-1000000000000
χ472-222-2-22-2-122-222-2-2-21111-1-1-1-22-2-2-2-22222-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-122-2-200000000-22-1-11111-1-1000000000000
χ482-222-2-22-2-122-222-2-2-21111-1-1-1-22-2-2-2-22222-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-1-2-222000000002-211-1-1-1-111000000000000
χ492-222-2-22-2-1-2-22-2-22221111-1-1-1-220000000011-1-11111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-2-220000000000-111-1−i3i3i3−i3000000000000
χ502-222-2-22-2-1-2-22-2-22221111-1-1-1-220000000011-1-11111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-222-200000000001-1-11i3−i3−i3i3000000000000
χ512-222-2-22-2-1-2-22-2-22221111-1-1-1-220000000011-1-11111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-2-220000000000-111-1i3−i3−i3i3000000000000
χ522-222-2-22-2-1-2-22-2-22221111-1-1-1-220000000011-1-11111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-222-200000000001-1-11−i3i3i3−i3000000000000
χ532-22-2-22-2222-2-200020-2-2222-2-20022−2−2−2−2222-2-220000000022−2−222−2−2−2−222−2−22200002i−2i−2i2i000000000000000000i2−i2−i2i20000
χ542-22-2-22-2222-2-200020-2-2222-2-20022−2−2−2−2222-2-220000000022−2−222−2−2−2−222−2−2220000−2i2i2i−2i000000000000000000−i2i2i2−i20000
χ552-22-2-22-2222-2-200020-2-2222-2-200−2−22222−2−22-2-2200000000−2−222−2−22222−2−222−2−200002i−2i−2i2i000000000000000000−i2i2i2−i20000
χ562-22-2-22-2222-2-200020-2-2222-2-200−2−22222−2−22-2-2200000000−2−222−2−22222−2−222−2−20000−2i2i2i−2i000000000000000000i2−i2−i2i20000
χ572-2-2-22-22220002-2-202-22-22-2-22002−22−2−22−220000002-2-22002−22−22−22−2−22−22−22−22000000002-2-22000000000000000000−222−2
χ582-2-2-22-22220002-2-202-22-22-2-22002−22−2−22−220000002-2-22002−22−22−22−2−22−22−22−2200000000-222-20000000000000000002−2−22
χ592-2-2-22-22220002-2-202-22-22-2-2200−22−222−22−20000002-2-2200−22−22−22−222−22−22−22−2000000002-2-220000000000000000002−2−22
χ602-2-2-22-22220002-2-202-22-22-2-2200−22−222−22−20000002-2-2200−22−22−22−222−22−22−22−200000000-222-2000000000000000000−222−2
χ6144444444-2444-4-4-44-4-2-2-2-2-2-2-2-4-400000000-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-400000000222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ63444-44-4-4-44-44-40004044-4-44-4-40000000000-44-440000000000000000000000000000000000000000000000000000000000
χ64444-44-4-4-4-24-44000-40-2-222-222002222−22−222222−22−22-22-2200000000−2−222−2−222−2−222−2−2220000000000000000000000000000000000
χ65444-44-4-4-4-24-44000-40-2-222-22200−22−222222−22−222222-22-220000000022−2−222−2−222−2−222−2−20000000000000000000000000000000000
χ66444-44-4-4-4-2-44-400040-2-222-22200000000002-22-200000000i6i6−i6−i6−i6−i6i6i6i6i6−i6−i6−i6−i6i6i60000000000000000000000000000000000
χ67444-44-4-4-4-2-44-400040-2-222-22200000000002-22-200000000−i6−i6i6i6i6i6−i6−i6−i6−i6i6i6i6i6−i6−i60000000000000000000000000000000000
χ6844-44-4-4-444000000004-4-44-44-4002-2-222-2-220000000000002-2-222-2-222-2-222-2-220000000000000000000000000000000000
χ6944-44-4-4-444000000004-4-44-44-400-222-2-222-2000000000000-222-2-222-2-222-2-222-20000000000000000000000000000000000
χ7044-44-4-4-44-200000000-222-22-22002-2-222-2-220000−2i32i30000−2i32i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i30000000000000000000000000000000000
χ7144-44-4-4-44-200000000-222-22-22002-2-222-2-2200002i3−2i300002i3−2i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i30000000000000000000000000000000000
χ7244-44-4-4-44-200000000-222-22-2200-222-2-222-20000−2i32i30000−2i32i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i30000000000000000000000000000000000
χ7344-44-4-4-44-200000000-222-22-2200-222-2-222-200002i3−2i300002i3−2i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i30000000000000000000000000000000000
χ7444-4-4-444-44000-44-4044-44-4-4-440000000000000000-44-440000000000000000000000000000000000000000000000000000
χ7544-4-4-444-4-20004-440-4-22-2222-20022−2222−2222−2222−22000000-22-2200−22−22−22−22−22−22−22−220000000000000000000000000000000000
χ7644-4-4-444-4-20004-440-4-22-2222-200−2222−2222−2222−2222000000-22-22002−22−22−22−22−22−22−22−20000000000000000000000000000000000
χ7744-4-4-444-4-2000-44-404-22-2222-200000000000000002-22-200i6−i6i6−i6−i6i6−i6i6i6−i6i6−i6−i6i6−i6i60000000000000000000000000000000000
χ7844-4-4-444-4-2000-44-404-22-2222-200000000000000002-22-200−i6i6−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6i6−i60000000000000000000000000000000000
χ794-444-4-44-4-244-4-4-44-442222-2-2-24-400000000-2-222-2-222-2-22200000000000000000000000000000000000000000000000000
χ804-444-4-44-4-2-4-4444-44-42222-2-2-24-40000000022-2-2-2-2-2-2222200000000000000000000000000000000000000000000000000
χ814-44-4-44-444-444000-40-4-4444-4-40000000000-444-40000000000000000000000000000000000000000000000000000000000
χ824-44-4-44-44-24-4-40004022-2-2-222002222−22−22−22−222222-222-200000000−2−222−2−22222−2−222−2−20000000000000000000000000000000000
χ834-44-4-44-44-24-4-40004022-2-2-22200−22−2222222222−22−22-222-20000000022−2−222−2−2−2−222−2−2220000000000000000000000000000000000
χ844-44-4-44-44-2-444000-4022-2-2-22200000000002-2-2200000000i6i6−i6−i6−i6−i6i6i6−i6−i6i6i6i6i6−i6−i60000000000000000000000000000000000
χ854-44-4-44-44-2-444000-4022-2-2-22200000000002-2-2200000000−i6−i6i6i6i6i6−i6−i6i6i6−i6−i6−i6−i6i6i60000000000000000000000000000000000
χ864-4-4444-4-4400000000-444-4-44-4002-2-22-222-20000000000002-2-222-2-22-222-2-222-20000000000000000000000000000000000
χ874-4-4444-4-4400000000-444-4-44-400-222-22-2-22000000000000-222-2-222-22-2-222-2-220000000000000000000000000000000000
χ884-4-4444-4-4-2000000002-2-222-22002-2-22-222-20000−2i32i300002i3−2i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i30000000000000000000000000000000000
χ894-4-4444-4-4-2000000002-2-222-22002-2-22-222-200002i3−2i30000−2i32i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i30000000000000000000000000000000000
χ904-4-4444-4-4-2000000002-2-222-2200-222-22-2-220000−2i32i300002i3−2i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i30000000000000000000000000000000000
χ914-4-4444-4-4-2000000002-2-222-2200-222-22-2-2200002i3−2i30000−2i32i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i30000000000000000000000000000000000
χ924-4-4-44-4444000-4440-4-44-44-4-440000000000000000-444-40000000000000000000000000000000000000000000000000000
χ934-4-4-44-444-20004-4-4042-22-222-20022−2222−22−2222−2222000000-222-200−22−22−22−222−22−22−22−20000000000000000000000000000000000
χ944-4-4-44-444-20004-4-4042-22-222-200−2222−222222−2222−22000000-222-2002−22−22−22−2−22−22−22−220000000000000000000000000000000000
χ954-4-4-44-444-2000-4440-42-22-222-200000000000000002-2-2200i6−i6i6−i6−i6i6−i6i6−i6i6−i6i6i6−i6i6−i60000000000000000000000000000000000
χ964-4-4-44-444-2000-4440-42-22-222-200000000000000002-2-2200−i6i6−i6i6i6−i6i6−i6i6−i6i6−i6−i6i6−i6i60000000000000000000000000000000000

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