Finite Group Databasebeta

← Group #10696436

Character table — Group #10696436

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444412121212121212122244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-11111-1-1-1-1
χ9222222222222-2-2-22-22222222-2-200000000-2-22222-2-2-2-2-2-20000000000000000000000000000220000-2-200000000
χ10222222222222-2-2-22-22222222-2-200000000-2-22222-2-2-2-2-2-20000000000000000000000000000-2-200002200000000
χ11222222222-2-2-2222-222222222-2-200000000-2-2-2-2-2-22222-2-200000000000000000000000000000022-2-20000000000
χ12222222222-2-2-2222-222222222-2-200000000-2-2-2-2-2-22222-2-2000000000000000000000000000000-2-2220000000000
χ13222222222-2-2-2-2-2-2-2-22222222220000000022-2-2-2-2-2-2-2-22200000000000000002-20022-2-200000000000000000000
χ14222222222-2-2-2-2-2-2-2-22222222220000000022-2-2-2-2-2-2-2-2220000000000000000-2200-2-22200000000000000000000
χ1522222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ1622222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ1722222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-111110000000000000000
χ1822222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-10000000000000000
χ1922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12200000000-1-111111111-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i32-200-1-111−i3−i3i3i30000000000000000
χ2022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12200000000-1-111111111-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3-220011-1-1i3i3−i3−i30000000000000000
χ2122222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12200000000-1-111111111-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i32-200-1-111i3i3−i3−i30000000000000000
χ2222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12200000000-1-111111111-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-220011-1-1−i3−i3i3i30000000000000000
χ23222-22-2-2-222-2-20002022-2-2-22-200−i2−i2−i2−i2i2i2i2i20022-2-2000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000000000000000002i−2i22−2−20000
χ24222-22-2-2-222-2-20002022-2-2-22-200−i2−i2−i2−i2i2i2i2i20022-2-2000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2000000000000000000−2i2i−2−2220000
χ25222-22-2-2-222-2-20002022-2-2-22-200i2i2i2i2−i2−i2−i2−i20022-2-2000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000000000000000002i−2i−2−2220000
χ26222-22-2-2-222-2-20002022-2-2-22-200i2i2i2i2−i2−i2−i2−i20022-2-2000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2000000000000000000−2i2i22−2−20000
χ2722-2-2-22-22200022-20-22-22-2-2-2200−i2−i2i2i2−i2−i2i2i200000022-2-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000002i−2i00000022−2−2
χ2822-2-2-22-22200022-20-22-22-2-2-2200−i2−i2i2i2−i2−i2i2i200000022-2-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000−2i2i000000−2−222
χ2922-2-2-22-22200022-20-22-22-2-2-2200i2i2−i2−i2i2i2−i2−i200000022-2-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000002i−2i000000−2−222
χ3022-2-2-22-22200022-20-22-22-2-2-2200i2i2−i2−i2i2i2−i2−i200000022-2-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000−2i2i00000022−2−2
χ312-22-2-2-22220002-220-2-22-22-2-2200−i2i2−i2i2−i2i2−i2i20000002-22-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000002i−2i000000002−22−2
χ322-22-2-2-22220002-220-2-22-22-2-2200−i2i2−i2i2−i2i2−i2i20000002-22-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000−2i2i00000000−22−22
χ332-22-2-2-22220002-220-2-22-22-2-2200i2−i2i2−i2i2−i2i2−i20000002-22-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000002i−2i00000000−22−22
χ342-22-2-2-22220002-220-2-22-22-2-2200i2−i2i2−i2i2−i2i2−i20000002-22-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000−2i2i000000002−22−2
χ352-2-222-2-22222-22-2-2-22-2-2-2-2222-222-2-222-2-22-2-22-22-22-2-22222-2-222-2-222-2-222-2-220000000000000000000000000000
χ362-2-222-2-22222-22-2-2-22-2-2-2-2222-22-222-2-222-2-2-22-22-22-2-2222-222-2-222-2-222-2-222-20000000000000000000000000000
χ372-2-222-2-22222-2-222-2-2-2-2-2-22222-200000000222-22-2-222-2-2-20000000000000000000000000000000000002i−2i2i−2i0000
χ382-2-222-2-22222-2-222-2-2-2-2-2-22222-200000000222-22-2-222-2-2-2000000000000000000000000000000000000−2i2i−2i2i0000
χ392-2-222-2-222-2-222-2-222-2-2-2-22222-20000000022-22-222-2-22-2-200000000000000000000000000000000000000002-2-22
χ402-2-222-2-222-2-222-2-222-2-2-2-22222-20000000022-22-222-2-22-2-20000000000000000000000000000000000000000-222-2
χ412-2-222-2-222-2-22-2222-2-2-2-2-2222-2200000000-2-2-22-22-222-2220000000000000000002-200002-22-20000000000000000
χ422-2-222-2-222-2-22-2222-2-2-2-2-2222-2200000000-2-2-22-22-222-222000000000000000000-220000-22-220000000000000000
χ432-2-222-2-22-122-22-2-2-221111-1-1-1-222-2-222-2-2211-11-11-111-1-1-1-111-1-111-1-111-1-111-10000−i3i3−i3i3−i3i3i3−i30000000000000000
χ442-2-222-2-22-122-22-2-2-221111-1-1-1-222-2-222-2-2211-11-11-111-1-1-1-111-1-111-1-111-1-111-10000i3−i3i3−i3i3−i3−i3i30000000000000000
χ452-2-222-2-22-122-22-2-2-221111-1-1-1-22-222-2-222-211-11-11-111-1-1-11-1-111-1-111-1-111-1-110000−i3i3−i3i3i3−i3−i3i30000000000000000
χ462-2-222-2-22-122-22-2-2-221111-1-1-1-22-222-2-222-211-11-11-111-1-1-11-1-111-1-111-1-111-1-110000i3−i3i3−i3−i3i3i3−i30000000000000000
χ472-2-222-2-22-1-2-22-2222-21111-1-1-1-2200000000111-11-11-1-11-1-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3002-2−i3i3i3−i3-11-110000000000000000
χ482-2-222-2-22-1-2-22-2222-21111-1-1-1-2200000000111-11-11-1-11-1-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i300-22i3−i3−i3i31-11-10000000000000000
χ492-2-222-2-22-1-2-22-2222-21111-1-1-1-2200000000111-11-11-1-11-1-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3002-2i3−i3−i3i3-11-110000000000000000
χ502-2-222-2-22-1-2-22-2222-21111-1-1-1-2200000000111-11-11-1-11-1-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i300-22−i3i3i3−i31-11-10000000000000000
χ512-2-2-2222-222-22000-20-2-222-22-200−i2i2i2−i2i2−i2−i2i2002-2-22000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000002-2000000−i2i2i2−i20000
χ522-2-2-2222-222-22000-20-2-222-22-200−i2i2i2−i2i2−i2−i2i2002-2-22000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000-22000000i2−i2−i2i20000
χ532-2-2-2222-222-22000-20-2-222-22-200i2−i2−i2i2−i2i2i2−i2002-2-22000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000002-2000000i2−i2−i2i20000
χ542-2-2-2222-222-22000-20-2-222-22-200i2−i2−i2i2−i2i2i2−i2002-2-22000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000-22000000−i2i2i2−i20000
χ5544444444-2444-4-4-44-4-2-2-2-2-2-2-2-4-40000000022-2-2-2-222222200000000000000000000000000000000000000000000
χ5644444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-400000000222222-2-2-2-22200000000000000000000000000000000000000000000
χ57444-44-4-4-44-444000-4044-4-4-44-4000000000000-4-44400000000000000000000000000000000000000000000000000
χ58444-44-4-4-4-24-4-400040-2-2222-2200−2i2−2i2−2i2−2i22i22i22i22i200-2-222000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000000000000000000000000000
χ59444-44-4-4-4-24-4-400040-2-2222-22002i22i22i22i2−2i2−2i2−2i2−2i200-2-222000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000000000000000000000000000
χ60444-44-4-4-4-2-444000-40-2-2222-2200000000000022-2-20000006666−6−6−6−6−6−6−6−666660000000000000000000000000000
χ61444-44-4-4-4-2-444000-40-2-2222-2200000000000022-2-2000000−6−6−6−666666666−6−6−6−60000000000000000000000000000
χ6244-44-4-44-44000000004-4-444-4-40022-2-2-2-22200000000000022-2-2-2-22222-2-2-2-2220000000000000000000000000000
χ6344-44-4-44-44000000004-4-444-4-400-2-22222-2-2000000000000-2-22222-2-2-2-22222-2-20000000000000000000000000000
χ6444-44-4-44-4-200000000-222-2-2220022-2-2-2-222−2i32i300000000−2i32i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i30000000000000000000000000000
χ6544-44-4-44-4-200000000-222-2-2220022-2-2-2-2222i3−2i3000000002i3−2i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i30000000000000000000000000000
χ6644-44-4-44-4-200000000-222-2-22200-2-22222-2-2−2i32i300000000−2i32i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i30000000000000000000000000000
χ6744-44-4-44-4-200000000-222-2-22200-2-22222-2-22i3−2i3000000002i3−2i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i30000000000000000000000000000
χ6844-4-4-44-444000-4-44044-44-4-4-440000000000000000-4-4440000000000000000000000000000000000000000000000
χ6944-4-4-44-44-200044-40-4-22-2222-200−2i2−2i22i22i2−2i2−2i22i22i2000000-2-22200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000000000000000
χ7044-4-4-44-44-200044-40-4-22-2222-2002i22i2−2i2−2i22i22i2−2i2−2i2000000-2-22200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000000000000000
χ7144-4-4-44-44-2000-4-4404-22-2222-2000000000000000022-2-20066−6−666−6−6−6−666−6−6660000000000000000000000000000
χ7244-4-4-44-44-2000-4-4404-22-2222-2000000000000000022-2-200−6−666−6−66666−6−666−6−60000000000000000000000000000
χ734-444-44-4-4400000000-444-44-4-4002-22-2-22-220000000000002-22-2-22-222-22-2-22-220000000000000000000000000000
χ744-444-44-4-4400000000-444-44-4-400-22-222-22-2000000000000-22-222-22-2-22-222-22-20000000000000000000000000000
χ754-444-44-4-4-2000000002-2-22-222002-22-2-22-22−2i32i3000000002i3−2i3−1+i31−i3−1+i31−i31−i3−1+i31−i3−1+i3−1−i31+i3−1−i31+i31+i3−1−i31+i3−1−i30000000000000000000000000000
χ764-444-44-4-4-2000000002-2-22-222002-22-2-22-222i3−2i300000000−2i32i3−1−i31+i3−1−i31+i31+i3−1−i31+i3−1−i3−1+i31−i3−1+i31−i31−i3−1+i31−i3−1+i30000000000000000000000000000
χ774-444-44-4-4-2000000002-2-22-22200-22-222-22-2−2i32i3000000002i3−2i31−i3−1+i31−i3−1+i3−1+i31−i3−1+i31−i31+i3−1−i31+i3−1−i3−1−i31+i3−1−i31+i30000000000000000000000000000
χ784-444-44-4-4-2000000002-2-22-22200-22-222-22-22i3−2i300000000−2i32i31+i3−1−i31+i3−1−i3−1−i31+i3−1−i31+i31−i3−1+i31−i3−1+i3−1+i31−i3−1+i31−i30000000000000000000000000000
χ794-44-4-4-4444000-44-404-44-44-4-440000000000000000-44-440000000000000000000000000000000000000000000000
χ804-44-4-4-444-20004-440-42-22-222-200−2i22i2−2i22i2−2i22i2−2i22i2000000-22-2200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ814-44-4-4-444-20004-440-42-22-222-2002i2−2i22i2−2i22i2−2i22i2−2i2000000-22-2200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ824-44-4-4-444-2000-44-4042-22-222-200000000000000002-22-2006−66−66−66−6−66−66−66−660000000000000000000000000000
χ834-44-4-4-444-2000-44-4042-22-222-200000000000000002-22-200−66−66−66−666−66−66−66−60000000000000000000000000000
χ844-4-444-4-44-244-4-444-4-42222-2-2-24-400000000-2-2-22-222-2-222200000000000000000000000000000000000000000000
χ854-4-444-4-44-2-4-444-4-4442222-2-2-24-400000000-2-22-22-2-222-22200000000000000000000000000000000000000000000
χ864-4-4-4444-44-44-400040-4-444-44-4000000000000-444-400000000000000000000000000000000000000000000000000
χ874-4-4-4444-4-24-44000-4022-2-22-2200−2i22i22i2−2i22i2−2i2−2i22i200-222-2000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000000000000000
χ884-4-4-4444-4-24-44000-4022-2-22-22002i2−2i2−2i22i2−2i22i22i2−2i200-222-2000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000000000000000
χ894-4-4-4444-4-2-44-40004022-2-22-220000000000002-2-220000006−6−66−666−6−666−66−6−660000000000000000000000000000
χ904-4-4-4444-4-2-44-40004022-2-22-220000000000002-2-22000000−666−66−6−666−6−66−666−60000000000000000000000000000

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