Finite Group Databasebeta

← Group #10698748

Character table — Group #10698748

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444412121212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
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
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1111111-1-1-1-1
χ9222222222222-2-2-22-22222222-2-2000000002222-2-2-2-2-2-2-2-20000000000000000000000000000002200-2-200000000
χ10222222222222-2-2-22-22222222-2-2000000002222-2-2-2-2-2-2-2-2000000000000000000000000000000-2-2002200000000
χ11222222222-2-2-2222-222222222-2-200000000-2-2-2-22222-2-2-2-200000000000000000000000000002200-2-20000000000
χ12222222222-2-2-2222-222222222-2-200000000-2-2-2-22222-2-2-2-20000000000000000000000000000-2-200220000000000
χ13222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-2222200000000000000002-20022-2-200000000000000000000
χ14222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-222220000000000000000-2200-2-22200000000000000000000
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
χ1922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i32-200-1-111−i3−i3i3i30000000000000000
χ2022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3-220011-1-1i3i3−i3−i30000000000000000
χ2122222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i32-200-1-111i3i3−i3−i30000000000000000
χ2222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-220011-1-1−i3−i3i3i30000000000000000
χ23222-22-2-2-2200022-20-222-22-2-2-2002222−2−2−2−2000022-2-200002222−2−2−2−22222−2−2−2−20000000000002-200000022−2−20000
χ24222-22-2-2-2200022-20-222-22-2-2-2002222−2−2−2−2000022-2-200002222−2−2−2−22222−2−2−2−2000000000000-22000000−2−2220000
χ25222-22-2-2-2200022-20-222-22-2-2-200−2−2−2−22222000022-2-20000−2−2−2−22222−2−2−2−222220000000000002-2000000−2−2220000
χ26222-22-2-2-2200022-20-222-22-2-2-200−2−2−2−22222000022-2-20000−2−2−2−22222−2−2−2−22222000000000000-2200000022−2−20000
χ2722-22-22-2-2222-2000-202-22-22-2-20022−2−222−2−222-2-20000000022−2−222−2−222−2−222−2−2000000000000002-20000000022−2−2
χ2822-22-22-2-2222-2000-202-22-22-2-20022−2−222−2−222-2-20000000022−2−222−2−222−2−222−2−200000000000000-2200000000−2−222
χ2922-22-22-2-2222-2000-202-22-22-2-200−2−222−2−22222-2-200000000−2−222−2−222−2−222−2−222000000000000002-200000000−2−222
χ3022-22-22-2-2222-2000-202-22-22-2-200−2−222−2−22222-2-200000000−2−222−2−222−2−222−2−22200000000000000-220000000022−2−2
χ312-22-2-222-222-22000-20-22-2-22-22002−22−22−22−22-22-2000000002−22−22−22−22−22−22−22−20000000000000000002i−2i0000−i2i2−i2i2
χ322-22-2-222-222-22000-20-22-2-22-22002−22−22−22−22-22-2000000002−22−22−22−22−22−22−22−2000000000000000000−2i2i0000i2−i2i2−i2
χ332-22-2-222-222-22000-20-22-2-22-2200−22−22−22−222-22-200000000−22−22−22−22−22−22−22−220000000000000000002i−2i0000i2−i2i2−i2
χ342-22-2-222-222-22000-20-22-2-22-2200−22−22−22−222-22-200000000−22−22−22−22−22−22−22−22000000000000000000−2i2i0000−i2i2−i2i2
χ352-2-222-22-220002-220-2-2-222-2-22002−2−22−222−200002-22-200002−2−22−222−22−2−22−222−200000000000000002i−2i00−i2i2−i2i20000
χ362-2-222-22-220002-220-2-2-222-2-22002−2−22−222−200002-22-200002−2−22−222−22−2−22−222−20000000000000000−2i2i00i2−i2i2−i20000
χ372-2-222-22-220002-220-2-2-222-2-2200−222−22−2−2200002-22-20000−222−22−2−22−222−22−2−2200000000000000002i−2i00i2−i2i2−i20000
χ382-2-222-22-220002-220-2-2-222-2-2200−222−22−2−2200002-22-20000−222−22−2−22−222−22−2−220000000000000000−2i2i00−i2i2−i2i20000
χ392-2-2-222-2222-2-22-2-222-2-2-2222-2-222-2-222-2-222-2-222-2-22-2-2222-2-222-2-222-2-222-2-220000000000000000000000000000
χ402-2-2-222-2222-2-22-2-222-2-2-2222-2-22-222-2-222-22-2-222-2-22-2-222-222-2-222-2-222-2-222-20000000000000000000000000000
χ412-2-2-222-2222-2-2-2222-2-2-2-2222-22-2000000002-2-22-222-222-2-200000000000000000000000000000000000000002i−2i−2i2i
χ422-2-2-222-2222-2-2-2222-2-2-2-2222-22-2000000002-2-22-222-222-2-20000000000000000000000000000000000000000−2i2i2i−2i
χ432-2-2-222-222-2222-2-2-22-2-2-2222-22-200000000-222-22-2-2222-2-20000000000000000000000000000000000002i−2i−2i2i0000
χ442-2-2-222-222-2222-2-2-22-2-2-2222-22-200000000-222-22-2-2222-2-2000000000000000000000000000000000000−2i2i2i−2i0000
χ452-2-2-222-222-222-222-2-2-2-2-2222-2-2200000000-222-2-222-2-2-2220000000000000000002i−2i00002i−2i2i−2i0000000000000000
χ462-2-2-222-222-222-222-2-2-2-2-2222-2-2200000000-222-2-222-2-2-222000000000000000000−2i2i0000−2i2i−2i2i0000000000000000
χ472-2-2-222-22-12-2-22-2-222111-1-1-11-222-2-222-2-22-111-1-111-111-1-1-111-1-111-1-111-1-111-100003−33−33−3−330000000000000000
χ482-2-2-222-22-12-2-22-2-222111-1-1-11-222-2-222-2-22-111-1-111-111-1-1-111-1-111-1-111-1-111-10000−33−33−333−30000000000000000
χ492-2-2-222-22-12-2-22-2-222111-1-1-11-22-222-2-222-2-111-1-111-111-1-11-1-111-1-111-1-111-1-1100003−33−3−333−30000000000000000
χ502-2-2-222-22-12-2-22-2-222111-1-1-11-22-222-2-222-2-111-1-111-111-1-11-1-111-1-111-1-111-1-110000−33−333−3−330000000000000000
χ512-2-2-222-22-1-222-222-2-2111-1-1-11-22000000001-1-111-1-1111-1-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3002i−2i3−3−33−ii−ii0000000000000000
χ522-2-2-222-22-1-222-222-2-2111-1-1-11-22000000001-1-111-1-1111-1-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i300−2i2i−333−3i−ii−i0000000000000000
χ532-2-2-222-22-1-222-222-2-2111-1-1-11-22000000001-1-111-1-1111-1-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3002i−2i−333−3−ii−ii0000000000000000
χ542-2-2-222-22-1-222-222-2-2111-1-1-11-22000000001-1-111-1-1111-1-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i300−2i2i3−3−33i−ii−i0000000000000000
χ5544444444-2444-4-4-44-4-2-2-2-2-2-2-2-4-400000000-2-2-2-22222222200000000000000000000000000000000000000000000
χ5644444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-4000000002222-2-2-2-2222200000000000000000000000000000000000000000000
χ57444-44-4-4-44000-4-440444-44-4-4-400000000000000-4-444000000000000000000000000000000000000000000000000
χ58444-44-4-4-4-200044-40-4-2-22-22220022222222−22−22−22−220000-2-2220000−2−2−2−22222−2−2−2−222220000000000000000000000000000
χ59444-44-4-4-4-200044-40-4-2-22-222200−22−22−22−22222222220000-2-22200002222−2−2−2−22222−2−2−2−20000000000000000000000000000
χ60444-44-4-4-4-2000-4-4404-2-22-22220000000000000022-2-20000i6i6i6i6−i6−i6−i6−i6−i6−i6−i6−i6i6i6i6i60000000000000000000000000000
χ61444-44-4-4-4-2000-4-4404-2-22-22220000000000000022-2-20000−i6−i6−i6−i6i6i6i6i6i6i6i6i6−i6−i6−i6−i60000000000000000000000000000
χ6244-44-44-4-44-4-44000404-44-44-4-40000000000-4-4440000000000000000000000000000000000000000000000000000
χ6344-44-44-4-4-244-4000-40-22-22-222002222−22−222222−22−22-2-22200000000−2−222−2−222−2−222−2−2220000000000000000000000000000
χ6444-44-44-4-4-244-4000-40-22-22-22200−22−222222−22−222222-2-2220000000022−2−222−2−222−2−222−2−20000000000000000000000000000
χ6544-44-44-4-4-2-4-4400040-22-22-222000000000022-2-200000000i6i6−i6−i6i6i6−i6−i6−i6−i6i6i6−i6−i6i6i60000000000000000000000000000
χ6644-44-44-4-4-2-4-4400040-22-22-222000000000022-2-200000000−i6−i6i6i6−i6−i6i6i6i6i6−i6−i6i6i6−i6−i60000000000000000000000000000
χ6744-4-4-4-4444000000004-4-4-4-4440022-2-2-2-22200000000000022-2-2-2-22222-2-2-2-2220000000000000000000000000000
χ6844-4-4-4-4444000000004-4-4-4-44400-2-22222-2-2000000000000-2-22222-2-2-2-22222-2-20000000000000000000000000000
χ6944-4-4-4-444-200000000-22222-2-20022-2-2-2-22200000000−2i32i3−2i32i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i30000000000000000000000000000
χ7044-4-4-4-444-200000000-22222-2-20022-2-2-2-222000000002i3−2i32i3−2i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i30000000000000000000000000000
χ7144-4-4-4-444-200000000-22222-2-200-2-22222-2-200000000−2i32i3−2i32i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i30000000000000000000000000000
χ7244-4-4-4-444-200000000-22222-2-200-2-22222-2-2000000002i3−2i32i3−2i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i30000000000000000000000000000
χ734-444-4-4-44400000000-444-4-44-4002-22-2-22-220000000000002-22-2-22-222-22-2-22-220000000000000000000000000000
χ744-444-4-4-44400000000-444-4-44-400-22-222-22-2000000000000-22-222-22-2-22-222-22-20000000000000000000000000000
χ754-444-4-4-44-2000000002-2-222-22002-22-2-22-2200000000−2i32i32i3−2i3−1+i31−i3−1+i31−i31−i3−1+i31−i3−1+i3−1−i31+i3−1−i31+i31+i3−1−i31+i3−1−i30000000000000000000000000000
χ764-444-4-4-44-2000000002-2-222-22002-22-2-22-22000000002i3−2i3−2i32i3−1−i31+i3−1−i31+i31+i3−1−i31+i3−1−i3−1+i31−i3−1+i31−i31−i3−1+i31−i3−1+i30000000000000000000000000000
χ774-444-4-4-44-2000000002-2-222-2200-22-222-22-200000000−2i32i32i3−2i31−i3−1+i31−i3−1+i3−1+i31−i3−1+i31−i31+i3−1−i31+i3−1−i3−1−i31+i3−1−i31+i30000000000000000000000000000
χ784-444-4-4-44-2000000002-2-222-2200-22-222-22-2000000002i3−2i3−2i32i31+i3−1−i31+i3−1−i3−1−i31+i3−1−i31+i31−i3−1+i31−i3−1+i3−1+i31−i3−1+i31−i30000000000000000000000000000
χ794-44-4-444-44-44-400040-44-4-44-440000000000-44-440000000000000000000000000000000000000000000000000000
χ804-44-4-444-4-24-44000-402-222-22-20022−2222−2222−2222−22-22-2200000000−22−22−22−22−22−22−22−220000000000000000000000000000
χ814-44-4-444-4-24-44000-402-222-22-200−2222−2222−2222−2222-22-22000000002−22−22−22−22−22−22−22−20000000000000000000000000000
χ824-44-4-444-4-2-44-4000402-222-22-200000000002-22-200000000i6−i6i6−i6i6−i6i6−i6−i6i6−i6i6−i6i6−i6i60000000000000000000000000000
χ834-44-4-444-4-2-44-4000402-222-22-200000000002-22-200000000−i6i6−i6i6−i6i6−i6i6i6−i6i6−i6i6−i6i6−i60000000000000000000000000000
χ844-4-444-44-44000-44-404-4-444-4-4400000000000000-44-44000000000000000000000000000000000000000000000000
χ854-4-444-44-4-20004-440-422-2-222-20022−22−2222−222222−220000-22-220000−222−22−2−22−222−22−2−220000000000000000000000000000
χ864-4-444-44-4-20004-440-422-2-222-200−222222−2222−22−22220000-22-2200002−2−22−222−22−2−22−222−20000000000000000000000000000
χ874-4-444-44-4-2000-44-40422-2-222-2000000000000002-22-20000i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ884-4-444-44-4-2000-44-40422-2-222-2000000000000002-22-20000−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ894-4-4-444-44-24-4-4-4444-4222-2-2-224-400000000-222-22-2-22-2-22200000000000000000000000000000000000000000000
χ904-4-4-444-44-2-4444-4-4-44222-2-2-224-4000000002-2-22-222-2-2-22200000000000000000000000000000000000000000000

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