Finite Group Databasebeta

← Group #10698731

Character table — Group #10698731

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444412121212121212122244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
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
χ9222222222222-2-2-22-22222222-2-2000000002222-2-2-2-2-2-2-2-200000000000000000000000000002200-2-20000000000
χ10222222222222-2-2-22-22222222-2-2000000002222-2-2-2-2-2-2-2-20000000000000000000000000000-2-200220000000000
χ11222222222-2-2-2222-222222222-2-200000000-2-2-2-22222-2-2-2-20000000000000000000000000000002200-2-200000000
χ12222222222-2-2-2222-222222222-2-200000000-2-2-2-22222-2-2-2-2000000000000000000000000000000-2-2002200000000
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
χ232222-2-2-2-2222-2000-20222-2-2-2-2002222−2−2−2−222-2-2000000002222−2−2−2−22222−2−2−2−20000000000002-200000022−2−20000
χ242222-2-2-2-2222-2000-20222-2-2-2-2002222−2−2−2−222-2-2000000002222−2−2−2−22222−2−2−2−2000000000000-22000000−2−2220000
χ252222-2-2-2-2222-2000-20222-2-2-2-200−2−2−2−2222222-2-200000000−2−2−2−22222−2−2−2−222220000000000002-2000000−2−2220000
χ262222-2-2-2-2222-2000-20222-2-2-2-200−2−2−2−2222222-2-200000000−2−2−2−22222−2−2−2−22222000000000000-2200000022−2−20000
χ2722-2-22-2-22200022-20-22-2-22-22-200−i2−i2i2i2−i2−i2i2i2000022-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000002-20000−i2−i2i2i2
χ2822-2-22-2-22200022-20-22-2-22-22-200−i2−i2i2i2−i2−i2i2i2000022-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000-220000i2i2−i2−i2
χ2922-2-22-2-22200022-20-22-2-22-22-200i2i2−i2−i2i2i2−i2−i2000022-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000002-20000i2i2−i2−i2
χ3022-2-22-2-22200022-20-22-2-22-22-200i2i2−i2−i2i2i2−i2−i2000022-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000-220000−i2−i2i2i2
χ312-22-2-22-2220002-220-2-22-22-2-2200−i2i2−i2i2−i2i2−i2i200002-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000002i−2i000000002−22−2
χ322-22-2-22-2220002-220-2-22-22-2-2200−i2i2−i2i2−i2i2−i2i200002-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000−2i2i00000000−22−22
χ332-22-2-22-2220002-220-2-22-22-2-2200i2−i2i2−i2i2−i2i2−i200002-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000002i−2i00000000−22−22
χ342-22-2-22-2220002-220-2-22-22-2-2200i2−i2i2−i2i2−i2i2−i200002-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000−2i2i000000002−22−2
χ352-2-2222-2-222-22000-20-2-22-2-222002−2−22−222−22-22-2000000002−2−22−222−22−2−22−222−200000000000000002i−2i00−i2i2−i2i20000
χ362-2-2222-2-222-22000-20-2-22-2-222002−2−22−222−22-22-2000000002−2−22−222−22−2−22−222−20000000000000000−2i2i00i2−i2i2−i20000
χ372-2-2222-2-222-22000-20-2-22-2-22200−222−22−2−222-22-200000000−222−22−2−22−222−22−2−2200000000000000002i−2i00i2−i2i2−i20000
χ382-2-2222-2-222-22000-20-2-22-2-22200−222−22−2−222-22-200000000−222−22−2−22−222−22−2−220000000000000000−2i2i00−i2i2−i2i20000
χ392-2-22-2-22222-2-22-2-222-2-2222-2-2-222-2-222-2-222-2-222-2-22-2-2222-2-222-2-222-2-222-2-220000000000000000000000000000
χ402-2-22-2-22222-2-22-2-222-2-2222-2-2-22-222-2-222-22-2-222-2-22-2-222-222-2-222-2-222-2-222-20000000000000000000000000000
χ412-2-22-2-22222-2-2-2222-2-2-2222-2-22-2000000002-2-22-222-222-2-20000000000000000000000000000000000002i−2i−2i2i0000
χ422-2-22-2-22222-2-2-2222-2-2-2222-2-22-2000000002-2-22-222-222-2-2000000000000000000000000000000000000−2i2i2i−2i0000
χ432-2-22-2-2222-2222-2-2-22-2-2222-2-22-200000000-222-22-2-2222-2-200000000000000000000000000000000000000002i−2i−2i2i
χ442-2-22-2-2222-2222-2-2-22-2-2222-2-22-200000000-222-22-2-2222-2-20000000000000000000000000000000000000000−2i2i2i−2i
χ452-2-22-2-2222-222-222-2-2-2-2222-2-2-2200000000-222-2-222-2-2-2220000000000000000002i−2i00002i−2i2i−2i0000000000000000
χ462-2-22-2-2222-222-222-2-2-2-2222-2-2-2200000000-222-2-222-2-2-222000000000000000000−2i2i0000−2i2i−2i2i0000000000000000
χ472-2-22-2-222-12-2-22-2-22211-1-1-111-222-2-222-2-22-111-1-111-111-1-1-111-1-111-1-111-1-111-100003−33−33−3−330000000000000000
χ482-2-22-2-222-12-2-22-2-22211-1-1-111-222-2-222-2-22-111-1-111-111-1-1-111-1-111-1-111-1-111-10000−33−33−333−30000000000000000
χ492-2-22-2-222-12-2-22-2-22211-1-1-111-22-222-2-222-2-111-1-111-111-1-11-1-111-1-111-1-111-1-1100003−33−3−333−30000000000000000
χ502-2-22-2-222-12-2-22-2-22211-1-1-111-22-222-2-222-2-111-1-111-111-1-11-1-111-1-111-1-111-1-110000−33−333−3−330000000000000000
χ512-2-22-2-222-1-222-222-2-211-1-1-111-22000000001-1-111-1-1111-1-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3002i−2i3−3−33−ii−ii0000000000000000
χ522-2-22-2-222-1-222-222-2-211-1-1-111-22000000001-1-111-1-1111-1-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i300−2i2i−333−3i−ii−i0000000000000000
χ532-2-22-2-222-1-222-222-2-211-1-1-111-22000000001-1-111-1-1111-1-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3002i−2i−333−3−ii−ii0000000000000000
χ542-2-22-2-222-1-222-222-2-211-1-1-111-22000000001-1-111-1-1111-1-1i3−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
χ574444-4-4-4-44-4-4400040444-4-4-4-40000000000-4-4440000000000000000000000000000000000000000000000000000
χ584444-4-4-4-4-244-4000-40-2-2-222220022222222−22−22−22−22-2-22200000000−2−2−2−22222−2−2−2−222220000000000000000000000000000
χ594444-4-4-4-4-244-4000-40-2-2-2222200−22−22−22−2222222222-2-222000000002222−2−2−2−22222−2−2−2−20000000000000000000000000000
χ604444-4-4-4-4-2-4-4400040-2-2-22222000000000022-2-200000000i6i6i6i6−i6−i6−i6−i6−i6−i6−i6−i6i6i6i6i60000000000000000000000000000
χ614444-4-4-4-4-2-4-4400040-2-2-22222000000000022-2-200000000−i6−i6−i6−i6i6i6i6i6i6i6i6i6−i6−i6−i6−i60000000000000000000000000000
χ6244-4-44-4-444000-4-44044-4-44-44-400000000000000-4-444000000000000000000000000000000000000000000000000
χ6344-4-44-4-44-200044-40-4-222-22-2200−2i2−2i22i22i2−2i2−2i22i22i20000-2-2220000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000000000000000
χ6444-4-44-4-44-200044-40-4-222-22-22002i22i2−2i2−2i22i22i2−2i2−2i20000-2-2220000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000000000000000
χ6544-4-44-4-44-2000-4-4404-222-22-220000000000000022-2-2000066−6−666−6−6−6−666−6−6660000000000000000000000000000
χ6644-4-44-4-44-2000-4-4404-222-22-220000000000000022-2-20000−6−666−6−66666−6−666−6−60000000000000000000000000000
χ6744-4-4-444-44000000004-4-4-44-44002i2i−2i−2i−2i−2i2i2i0000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ6844-4-4-444-44000000004-4-4-44-4400−2i−2i2i2i2i2i−2i−2i000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ6944-4-4-444-4-200000000-2222-22-2002i2i−2i−2i−2i−2i2i2i00000000−2i32i3−2i32i32ζ142ζ14−2ζ14−2ζ14−2ζ14−2ζ142ζ142ζ142ζ222ζ22−2ζ22−2ζ22−2ζ22−2ζ222ζ222ζ220000000000000000000000000000
χ7044-4-4-444-4-200000000-2222-22-2002i2i−2i−2i−2i−2i2i2i000000002i3−2i32i3−2i32ζ222ζ22−2ζ22−2ζ22−2ζ22−2ζ222ζ222ζ222ζ142ζ14−2ζ14−2ζ14−2ζ14−2ζ142ζ142ζ140000000000000000000000000000
χ7144-4-4-444-4-200000000-2222-22-200−2i−2i2i2i2i2i−2i−2i00000000−2i32i3−2i32i3−2ζ14−2ζ142ζ142ζ142ζ142ζ14−2ζ14−2ζ14−2ζ22−2ζ222ζ222ζ222ζ222ζ22−2ζ22−2ζ220000000000000000000000000000
χ7244-4-4-444-4-200000000-2222-22-200−2i−2i2i2i2i2i−2i−2i000000002i3−2i32i3−2i3−2ζ22−2ζ222ζ222ζ222ζ222ζ22−2ζ22−2ζ22−2ζ14−2ζ142ζ142ζ142ζ142ζ14−2ζ14−2ζ140000000000000000000000000000
χ734-44-44-44-4400000000-44-4-444-4002i−2i2i−2i−2i2i−2i2i0000000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ744-44-44-44-4400000000-44-4-444-400−2i2i−2i2i2i−2i2i−2i000000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ754-44-44-44-4-2000000002-222-2-22002i−2i2i−2i−2i2i−2i2i00000000−2i32i32i3−2i32ζ22−2ζ222ζ22−2ζ22−2ζ222ζ22−2ζ222ζ222ζ14−2ζ142ζ14−2ζ14−2ζ142ζ14−2ζ142ζ140000000000000000000000000000
χ764-44-44-44-4-2000000002-222-2-22002i−2i2i−2i−2i2i−2i2i000000002i3−2i3−2i32i32ζ14−2ζ142ζ14−2ζ14−2ζ142ζ14−2ζ142ζ142ζ22−2ζ222ζ22−2ζ22−2ζ222ζ22−2ζ222ζ220000000000000000000000000000
χ774-44-44-44-4-2000000002-222-2-2200−2i2i−2i2i2i−2i2i−2i00000000−2i32i32i3−2i3−2ζ222ζ22−2ζ222ζ222ζ22−2ζ222ζ22−2ζ22−2ζ142ζ14−2ζ142ζ142ζ14−2ζ142ζ14−2ζ140000000000000000000000000000
χ784-44-44-44-4-2000000002-222-2-2200−2i2i−2i2i2i−2i2i−2i000000002i3−2i3−2i32i3−2ζ142ζ14−2ζ142ζ142ζ14−2ζ142ζ14−2ζ14−2ζ222ζ22−2ζ222ζ222ζ22−2ζ222ζ22−2ζ220000000000000000000000000000
χ794-44-4-44-444000-44-404-44-44-4-4400000000000000-44-44000000000000000000000000000000000000000000000000
χ804-44-4-44-44-20004-440-42-22-222-200−2i22i2−2i22i2−2i22i2−2i22i20000-22-220000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ814-44-4-44-44-20004-440-42-22-222-2002i2−2i22i2−2i22i2−2i22i2−2i20000-22-220000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ824-44-4-44-44-2000-44-4042-22-222-2000000000000002-22-200006−66−66−66−6−66−66−66−660000000000000000000000000000
χ834-44-4-44-44-2000-44-4042-22-222-2000000000000002-22-20000−66−66−66−666−66−66−66−60000000000000000000000000000
χ844-4-4444-4-44-44-400040-4-44-4-4440000000000-44-440000000000000000000000000000000000000000000000000000
χ854-4-4444-4-4-24-44000-4022-222-2-20022−22−2222−222222−22-22-2200000000−222−22−2−22−222−22−2−220000000000000000000000000000
χ864-4-4444-4-4-24-44000-4022-222-2-200−222222−2222−22−2222-22-22000000002−2−22−222−22−2−22−222−20000000000000000000000000000
χ874-4-4444-4-4-2-44-40004022-222-2-200000000002-22-200000000i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ884-4-4444-4-4-2-44-40004022-222-2-200000000002-22-200000000−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ894-4-44-4-444-24-4-4-4444-422-2-2-2224-400000000-222-22-2-22-2-22200000000000000000000000000000000000000000000
χ904-4-44-4-444-2-4444-4-4-4422-2-2-2224-4000000002-2-22-222-2-2-22200000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.