Finite Group Databasebeta

← Group #10830071

Character table — Group #10830071

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order12222222344446666666444444121212121212121222444666688881212121212122424242424242424444444412121212222222488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-11-1-1-1-1-1
χ41111111111111111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111111
χ5111111111111111111111111-1-111-1-1-1-111-1-1-111-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-11111-1-111-111-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-1-111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-111-1-11-1-1111
χ7111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1111-1-111-1-1-1-1-1-1-1111
χ8111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-11111111-1-1-1
χ911111111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1
χ1111111111111111111111-1-1-1-11111111111-1-11-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-111111-1
χ1211111111111111111111-1-1-1-11111111111-1-11-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-11111-1111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-11111-1111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11111-1-1-1-1111-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-1-1-1-111-1-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-1111-1-111-1
χ17222222222-2-2-2-22222222000022-2-22222-2-200-200000000000000-2-20000000022-2-22200000000000-200000
χ18222222222-2-2-2-22222222000022-2-22222-2-200-200000000000000-2-200000000-2-222-2-200000000000200000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-200200000000000000220000000022-2-2-2-200000000000200000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2002000000000000002200000000-2-2222200000000000-200000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-222111122-2-2-1-1-1-111-1-1-1-11111000000-211-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-2-2-21111-2-222-1-1-1-1111111-1-1-1-10000002-1-111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-22221111-2-2-2-21111-1-1111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-22-2-2111122221111-1-1-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-222-1-1-1-1-2-2221111111111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-2-2-2-1-1-1-122-2-2111111-1-1-1-111110000002-1-111000000000000
χ292222-2-2-2-22-22-2222-22-2-2-22i2i−2i−2i00-2-200002200000000000002i2i−2i−2i00000000000000000000000002-202i−2i000
χ302222-2-2-2-22-22-2222-22-2-2-22i2i−2i−2i00-2-200002200000000000002i2i−2i−2i0000000000000000000000000-220−2i2i000
χ312222-2-2-2-22-22-2222-22-2-2-2−2i−2i2i2i00-2-20000220000000000000−2i−2i2i2i00000000000000000000000002-20−2i2i000
χ322222-2-2-2-22-22-2222-22-2-2-2−2i−2i2i2i00-2-20000220000000000000−2i−2i2i2i0000000000000000000000000-2202i−2i000
χ332-2-2222-2-2222-2-2-2-2222-2-22i−2i2i−2i002-200002-20002i−2i00002-2002i−2i2i−2i0022-2-200000000000002i−2i000000000000
χ342-2-2222-2-2222-2-2-2-2222-2-22i−2i2i−2i002-200002-2000−2i2i0000-22002i−2i2i−2i00-2-2220000000000000−2i2i000000000000
χ352-2-2222-2-2222-2-2-2-2222-2-2−2i2i−2i2i002-200002-20002i−2i0000-2200−2i2i−2i2i00-2-22200000000000002i−2i000000000000
χ362-2-2222-2-2222-2-2-2-2222-2-2−2i2i−2i2i002-200002-2000−2i2i00002-200−2i2i−2i2i0022-2-20000000000000−2i2i000000000000
χ372-2-2222-2-2-122-2-211-1-1-1112i−2i2i−2i00-1133−3−3-110002i−2i−i3−i3i3i32-200−ii−ii3−3-1-11133−3−30000000−i3i3−ii000000000000
χ382-2-2222-2-2-122-2-211-1-1-1112i−2i2i−2i00-1133−3−3-11000−2i2i−i3−i3i3i3-2200−ii−ii3−311-1-1−3−3330000000i3−i3i−i000000000000
χ392-2-2222-2-2-122-2-211-1-1-1112i−2i2i−2i00-11−3−333-110002i−2ii3i3−i3−i32-200−ii−ii−33-1-111−3−3330000000i3−i3−ii000000000000
χ402-2-2222-2-2-122-2-211-1-1-1112i−2i2i−2i00-11−3−333-11000−2i2ii3i3−i3−i3-2200−ii−ii−3311-1-133−3−30000000−i3i3i−i000000000000
χ412-2-2222-2-2-122-2-211-1-1-111−2i2i−2i2i00-1133−3−3-110002i−2ii3i3−i3−i3-2200i−ii−i3−311-1-1−3−3330000000−i3i3−ii000000000000
χ422-2-2222-2-2-122-2-211-1-1-111−2i2i−2i2i00-1133−3−3-11000−2i2ii3i3−i3−i32-200i−ii−i3−3-1-11133−3−30000000i3−i3i−i000000000000
χ432-2-2222-2-2-122-2-211-1-1-111−2i2i−2i2i00-11−3−333-110002i−2i−i3−i3i3i3-2200i−ii−i−3311-1-133−3−30000000i3−i3−ii000000000000
χ442-2-2222-2-2-122-2-211-1-1-111−2i2i−2i2i00-11−3−333-11000−2i2i−i3−i3i3i32-200i−ii−i−33-1-111−3−3330000000−i3i3i−i000000000000
χ452-2-22-2-22222-2-22-2-2-22-2220000002-20000-222-20002-22-20000000000000000002-22-20000000002-200000000
χ462-2-22-2-22222-2-22-2-2-22-2220000002-20000-222-20002-22-2000000000000000000-22-22000000000-2200000000
χ472-2-22-2-22222-2-22-2-2-22-2220000002-20000-22-22000-22-220000000000000000002-22-2000000000-2200000000
χ482-2-22-2-22222-2-22-2-2-22-2220000002-20000-22-22000-22-22000000000000000000-22-220000000002-200000000
χ492-2-22-2-2222-222-2-2-2-22-2222-2-2200-2200002-200000000000002-2-2200000000002-2-2200000002-20000000000
χ502-2-22-2-2222-222-2-2-2-22-2222-2-2200-2200002-200000000000002-2-220000000000-222-20000000-220000000000
χ512-2-22-2-2222-222-2-2-2-22-222-222-200-2200002-20000000000000-222-200000000002-2-220000000-220000000000
χ522-2-22-2-2222-222-2-2-2-22-222-222-200-2200002-20000000000000-222-20000000000-222-200000002-20000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200004422-2-2-2-22200-400000000000000220000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-42222222200400000000000000-2-20000000000000000000000000000000
χ554444-4-4-4-444-44-444-44-4-4-4000000440000-4-400000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-24-44-4-2-22-2222000000-2-200002200000−2i32i32i3−2i300000000000000000000000000000000000000000
χ574444-4-4-4-4-24-44-4-2-22-2222000000-2-2000022000002i3−2i3−2i32i300000000000000000000000000000000000000000
χ584444-4-4-4-4-2-44-44-2-22-22224i4i−4i−4i00220000-2-20000000000000−2i−2i2i2i000000000000000000000000000000000
χ594444-4-4-4-4-2-44-44-2-22-2222−4i−4i4i4i00220000-2-200000000000002i2i−2i−2i000000000000000000000000000000000
χ6044-4-44-44-4400004-4-4-444-40000000000000000000000000000000000000000000004-400000000000000000
χ6144-4-44-44-4400004-4-4-444-4000000000000000000000000000000000000000000000-4400000000000000000
χ6244-4-4-44-44400004-44-4-4-44000000000000000000000000022−22000000000022−2222−2200000000000000000000000
χ6344-4-4-44-44400004-44-4-4-440000000000000000000000000−22220000000000−2222−222200000000000000000000000
χ6444-4-4-44-44-20000-22-2222-20000000023−2323−23000000000000022−220000006−66−6−22−2200000000000000000000000
χ6544-4-4-44-44-20000-22-2222-20000000023−2323−230000000000000−2222000000−66−662−22−200000000000000000000000
χ6644-4-4-44-44-20000-22-2222-200000000−2323−2323000000000000022−22000000−66−66−22−2200000000000000000000000
χ6744-4-4-44-44-20000-22-2222-200000000−2323−23230000000000000−22220000006−66−62−22−200000000000000000000000
χ684-44-44-4-4440000-44-4-44-44000000000000000000000000000000000000000000000000000000000000022−220
χ694-44-44-4-4440000-44-4-44-440000000000000000000000000000000000000000000000000000000000000−22220
χ704-44-4-444-440000-444-4-44-400004-4004-4-440000000000000000000000000000000000000000000000000000
χ714-44-4-444-440000-444-4-44-40000-4400-444-40000000000000000000000000000000000000000000000000000
χ724-44-4-444-4-200002-2-222-2200004-400-222-20000000000000000000006−6−66−666−600000000000000000000000
χ734-44-4-444-4-200002-2-222-2200004-400-222-2000000000000000000000−666−66−6−6600000000000000000000000
χ744-44-4-444-4-200002-2-222-220000-44002-2-220000000000000000000006−6−666−6−6600000000000000000000000
χ754-44-4-444-4-200002-2-222-220000-44002-2-22000000000000000000000−666−6−666−600000000000000000000000
χ764-4-4444-4-44-4-444-4-4444-4-4000000-440000-4400000000000000000000000000000000000000000000000000
χ774-4-4444-4-4-2-4-44422-2-2-2220000002-22323−23−232-200000000000000000−23230000000000000000000000000000000
χ784-4-4444-4-4-2-4-44422-2-2-2220000002-2−23−2323232-20000000000000000023−230000000000000000000000000000000
χ794-4-44-4-444-24-4-44222-22-2-2000000-2200002-24-4000-22-2200000000000000000000000000000000000000000
χ804-4-44-4-444-24-4-44222-22-2-2000000-2200002-2-440002-22-200000000000000000000000000000000000000000
χ814-4-44-4-444-2-444-4222-22-2-24-4-44002-20000-220000000000000-222-2000000000000000000000000000000000
χ824-4-44-4-444-2-444-4222-22-2-2-444-4002-20000-2200000000000002-2-22000000000000000000000000000000000
χ8388-8-88-88-8-40000-4444-4-440000000000000000000000000000000000000000000000000000000000000000
χ848-88-88-8-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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