Finite Group Databasebeta

← Group #10696451

Character table — Group #10696451

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order12222222344444444666666644121212121212121222446666888812121212121224242424242424248888888844121212124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9222222222222-2-2-22-22222222-2-2222-2-2-2-2222-2-222220000-2-2-2-2-2-200000000000000000000000000000000
χ10222222222222-2-2-22-22222222-2-2222-2-2-2-22-2-222-2-2-2-20000-2-2222200000000000000000000000000000000
χ11222222222-2-2-2222-222222222-2-2-2-2-22222-2000000000000-2-20000000000000000000000000022-2-2000000
χ12222222222-2-2-2222-222222222-2-2-2-2-22222-2000000000000-2-200000000000000000000000000-2-222000000
χ13222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000000002200000000000000000000000000000000002-2
χ14222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000220000000000000000000000000000000000-22
χ1522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ1622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-11111111100000000-2-211110000000000
χ1722222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ1822222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-11111111111110000000022-1-1-1-10000000000
χ1922222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2-1-1-1-10000111111−i3−i3−i3−i3i3i3i3i30000000000−i3−i3i3i30000000000
χ2022222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2-1-1-1-10000111111i3i3i3i3−i3−i3−i3−i30000000000i3i3−i3−i30000000000
χ2122222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2221111000011-1-1-1-1−i3−i3−i3−i3i3i3i3i30000000000i3i3−i3−i30000000000
χ2222222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2221111000011-1-1-1-1i3i3i3i3−i3−i3−i3−i30000000000−i3−i3i3i30000000000
χ232222-2-2-2-2222-2000-2022-2-22-2-20022-20000-22-20022-2-20000000000000000002222−2−2−2−2000000000022−2−200
χ242222-2-2-2-2222-2000-2022-2-22-2-20022-20000-22-20022-2-2000000000000000000−2−2−2−222220000000000−2−22200
χ252222-2-2-2-2222-2000-2022-2-22-2-20022-20000-2-2200-2-2220000000000000000002222−2−2−2−20000000000−2−22200
χ262222-2-2-2-2222-2000-2022-2-22-2-20022-20000-2-2200-2-222000000000000000000−2−2−2−22222000000000022−2−200
χ2722-2-2-22-2220002-2-2022-22-2-2-220000022-2-200000000022−2−200000022−2−222−2−222−2−222−2−2000000002-2000000
χ2822-2-2-22-2220002-2-2022-22-2-2-220000022-2-200000000022−2−200000022−2−222−2−2−2−222−2−22200000000-22000000
χ2922-2-2-22-2220002-2-2022-22-2-2-220000022-2-2000000000−2−222000000−2−222−2−22222−2−222−2−200000000-22000000
χ3022-2-2-22-2220002-2-2022-22-2-2-220000022-2-2000000000−2−222000000−2−222−2−222−2−222−2−222000000002-2000000
χ312-22-2-2-2222000-22-202-22-22-2-22000002-22-20000000002−22−20000002−22−22−22−22−22−22−22−20000002-200000000
χ322-22-2-2-2222000-22-202-22-22-2-22000002-22-20000000002−22−20000002−22−22−22−2−22−22−22−22000000-2200000000
χ332-22-2-2-2222000-22-202-22-22-2-22000002-22-2000000000−22−22000000−22−22−22−222−22−22−22−2000000-2200000000
χ342-22-2-2-2222000-22-202-22-22-2-22000002-22-2000000000−22−22000000−22−22−22−22−22−22−22−220000002-200000000
χ352-2-222-2-2222-2222-2-2-2-2-2-2-22222-22-22-222-2-20000000000002-20000000000000000000000000000002i−2i2i−2i00
χ362-2-222-2-2222-2222-2-2-2-2-2-2-22222-22-22-222-2-20000000000002-2000000000000000000000000000000−2i2i−2i2i00
χ372-2-222-2-2222-22-2-22-22-2-2-2-2222-222-222-2-22-2000000000000-220000000000002-2-222-2-220000000000000000
χ382-2-222-2-2222-22-2-22-22-2-2-2-2222-222-222-2-22-2000000000000-22000000000000-222-2-222-20000000000000000
χ392-2-222-2-222-22-222-22-2-2-2-2-2222-22-22-2-222-22000000000000-22000000000000000000002-22-22-20000000000
χ402-2-222-2-222-22-222-22-2-2-2-2-2222-22-22-2-222-22000000000000-2200000000000000000000-22-22-220000000000
χ412-2-222-2-222-22-2-2-2222-2-2-2-22222-2-22-22-2-222000000002-2-222-200002-2-222-2-22000000000000000000000000
χ422-2-222-2-222-22-2-2-2222-2-2-2-22222-2-22-22-2-22200000000-222-22-20000-222-2-222-2000000000000000000000000
χ432-2-222-2-22-1-22-222-22-21111-1-1-1-221-111-1-11-10000−i3i3−i3i300001-1−i3−i3i3i3−i3i3i3−i3i3−i3−i3i3000000002-2-11-110000000000
χ442-2-222-2-22-1-22-222-22-21111-1-1-1-221-111-1-11-10000−i3i3−i3i300001-1−i3−i3i3i3i3−i3−i3i3−i3i3i3−i300000000-221-11-10000000000
χ452-2-222-2-22-1-22-222-22-21111-1-1-1-221-111-1-11-10000i3−i3i3−i300001-1i3i3−i3−i3−i3i3i3−i3i3−i3−i3i300000000-221-11-10000000000
χ462-2-222-2-22-1-22-222-22-21111-1-1-1-221-111-1-11-10000i3−i3i3−i300001-1i3i3−i3−i3i3−i3−i3i3−i3i3i3−i3000000002-2-11-110000000000
χ472-2-222-2-22-1-22-2-2-22221111-1-1-12-21-11-111-1-10000−i3i3−i3i32-2-22-11i3i3−i3−i3-111-1-111-10000000000−i3i3i3−i30000000000
χ482-2-222-2-22-1-22-2-2-22221111-1-1-12-21-11-111-1-10000−i3i3−i3i3-222-2-11i3i3−i3−i31-1-111-1-110000000000i3−i3−i3i30000000000
χ492-2-222-2-22-1-22-2-2-22221111-1-1-12-21-11-111-1-10000i3−i3i3−i32-2-22-11−i3−i3i3i3-111-1-111-10000000000i3−i3−i3i30000000000
χ502-2-222-2-22-1-22-2-2-22221111-1-1-12-21-11-111-1-10000i3−i3i3−i3-222-2-11−i3−i3i3i31-1-111-1-110000000000−i3i3i3−i30000000000
χ512-2-22-222-222-2-200020-2-2222-2-2002-2-200002002i−2i00000000002i−2i2i−2i000000002−2−22−222−20000000000−i2i2i2−i200
χ522-2-22-222-222-2-200020-2-2222-2-2002-2-200002002i−2i00000000002i−2i2i−2i00000000−222−22−2−220000000000i2−i2−i2i200
χ532-2-22-222-222-2-200020-2-2222-2-2002-2-20000200−2i2i0000000000−2i2i−2i2i000000002−2−22−222−20000000000i2−i2−i2i200
χ542-2-22-222-222-2-200020-2-2222-2-2002-2-20000200−2i2i0000000000−2i2i−2i2i00000000−222−22−2−220000000000−i2i2i2−i200
χ5544444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000000022000000000000000000000000000000000000
χ5644444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222000000000000-2-2000000000000000000000000000000000000
χ574444-4-4-4-44-4-440004044-4-44-4-400-4-440000400000000000000000000000000000000000000000000000000
χ584444-4-4-4-4-244-4000-40-2-222-22200-2-22000024-400-2-222000000000000000000000000000000000000000000
χ594444-4-4-4-4-244-4000-40-2-222-22200-2-2200002-440022-2-2000000000000000000000000000000000000000000
χ604444-4-4-4-4-2-4-4400040-2-222-2220022-20000-20000000000000023−23−232300000000000000000000000000000000
χ614444-4-4-4-4-2-4-4400040-2-222-2220022-20000-200000000000000−232323−2300000000000000000000000000000000
χ6244-4-44-44-44000000004-4-44-44-400000000000000000000000000000000000022-2-2-2-2220000000000000000
χ6344-4-44-44-44000000004-4-44-44-4000000000000000000000000000000000000-2-22222-2-20000000000000000
χ6444-4-4-44-444000-4440-44-44-4-4-4400000-4-444000000000000000000000000000000000000000000000000000
χ6544-4-4-44-44-20004-4-404-22-2222-200000-2-2220000000002222−22−22000000−2−222−2−222000000000000000000000000
χ6644-4-4-44-44-20004-4-404-22-2222-200000-2-222000000000−22−22222200000022−2−222−2−2000000000000000000000000
χ6744-4-4-44-44-2000-4440-4-22-2222-20000022-2-20000000000000000000i6i6−i6−i6−i6−i6i6i6000000000000000000000000
χ6844-4-4-44-44-2000-4440-4-22-2222-20000022-2-20000000000000000000−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ694-44-444-4-4400000000-444-4-44-40000000000000000000000000000000000002-22-2-22-220000000000000000
χ704-44-444-4-4400000000-444-4-44-4000000000000000000000000000000000000-22-222-22-20000000000000000
χ714-44-4-4-44440004-440-4-44-44-4-4400000-44-44000000000000000000000000000000000000000000000000000
χ724-44-4-4-444-20004-440-42-22-222-2000002-22-20000000000000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ734-44-4-4-444-20004-440-42-22-222-2000002-22-20000000000000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ744-44-4-4-444-2000-44-4042-22-222-200000-22-2200000000022−2222−22000000−22−22−22−22000000000000000000000000
χ754-44-4-4-444-2000-44-4042-22-222-200000-22-22000000000−2222−22220000002−22−22−22−2000000000000000000000000
χ764-4-444-4-44-24-4444-4-4-42222-2-2-24-4-22-22-2-222000000000000-22000000000000000000000000000000000000
χ774-4-444-4-44-24-44-4-44-442222-2-2-2-44-22-2-222-220000000000002-2000000000000000000000000000000000000
χ784-4-44-444-44-444000-40-4-4444-4-400-4440000-400000000000000000000000000000000000000000000000000
χ794-4-44-444-4-24-4-40004022-2-2-22200-2220000-2004i−4i0000000000−2i2i−2i2i00000000000000000000000000000000
χ804-4-44-444-4-24-4-40004022-2-2-22200-2220000-200−4i4i00000000002i−2i2i−2i00000000000000000000000000000000
χ814-4-44-444-4-2-444000-4022-2-2-222002-2-2000020000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ824-4-44-444-4-2-444000-4022-2-2-222002-2-20000200002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ8388-8-88-88-8-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000
χ848-88-888-8-8-4000000004-4-444-44000000000000000000000000000000000000000000000000000000000000

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