Finite Group Databasebeta

← Group #10859058

Character table — Group #10859058

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424224444412121212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ5111111111111111111111111-1-1-1-1-1-11111-1-1-111-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-111-1-1-1-1-1111111-1-1-1
χ6111111111111111111111111-1-1-1-1-1-11111-1-1-111-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-111-1-1111-1-1-1-1-1-1111
χ7111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11-1-111-1-1-111-1-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-111111-1-11111-1-1-1
χ911111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ1011111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1
χ1111111111111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ1211111111111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-11111-1111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-111-1-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-11111-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-11-1-111-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-11-1-111-111-1-1-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1111-1-11111-1-111-1
χ17222222222-2-2-2-222222220000222222-2-2-2-2-20000000000000000-2-20000000022-2-2-2-200000200000000000
χ18222222222-2-2-2-222222220000222222-2-2-2-2-20000000000000000-2-200000000-2-2222200000-200000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-220000000000000000220000000022-2-22200000-200000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2200000000000000002200000000-2-222-2-200000200000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-2-222-2-2221111-1-1-1-111-1-1-1-11111000000-2-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-2-2-2-222-2-21111-1-1-1-1111111-1-1-1-1000000211-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-222-2-2-2-211111111-1-1111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-2222222-2-2-1-1-1-11111111111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-222-2-2-2-222-1-1-1-1111111-1-1-1-11111000000211-1-1000000000000
χ2922-2-222-2-2222-2-222-2-2-22-2000000000022-2-202-200000022-2-2000000000000002-22-2000000002-2000000000
χ3022-2-222-2-2222-2-222-2-2-22-2000000000022-2-202-200000022-2-200000000000000-22-2200000000-22000000000
χ3122-2-222-2-2222-2-222-2-2-22-2000000000022-2-20-22000000-2-222000000000000002-22-200000000-22000000000
χ3222-2-222-2-2222-2-222-2-2-22-2000000000022-2-20-22000000-2-22200000000000000-22-22000000002-2000000000
χ3322-2-222-2-22-2-22222-2-2-22-22i2i−2i−2i000000-2-22200000000000002i2i−2i−2i00000000002-2-2200000000002i−2i0000000
χ3422-2-222-2-22-2-22222-2-2-22-22i2i−2i−2i000000-2-22200000000000002i2i−2i−2i0000000000-222-20000000000−2i2i0000000
χ3522-2-222-2-22-2-22222-2-2-22-2−2i−2i2i2i000000-2-2220000000000000−2i−2i2i2i00000000002-2-220000000000−2i2i0000000
χ3622-2-222-2-22-2-22222-2-2-22-2−2i−2i2i2i000000-2-2220000000000000−2i−2i2i2i0000000000-222-200000000002i−2i0000000
χ372-22-22-2-2222-22-2-2-22-222-22i−2i2i−2i0000002-22-20002-2002i−2i00002i−2i2i−2i002i2i−2i−2i000000000002-200000000000000
χ382-22-22-2-2222-22-2-2-22-222-22i−2i2i−2i0000002-22-2000-2200−2i2i00002i−2i2i−2i00−2i−2i2i2i00000000000-2200000000000000
χ392-22-22-2-2222-22-2-2-22-222-2−2i2i−2i2i0000002-22-20002-200−2i2i0000−2i2i−2i2i00−2i−2i2i2i000000000002-200000000000000
χ402-22-22-2-2222-22-2-2-22-222-2−2i2i−2i2i0000002-22-2000-22002i−2i0000−2i2i−2i2i002i2i−2i−2i00000000000-2200000000000000
χ412-22-22-2-22-12-22-211-11-1-112i−2i2i−2i0033−3−3-11-110002-2002i−2i−i3i3−i3i3−ii−ii3−3−i−iii−i3−i3i3i30000000-113−3000000000000
χ422-22-22-2-22-12-22-211-11-1-112i−2i2i−2i0033−3−3-11-11000-2200−2i2i−i3i3−i3i3−ii−ii3−3ii−i−ii3i3−i3−i300000001-1−33000000000000
χ432-22-22-2-22-12-22-211-11-1-112i−2i2i−2i00−3−333-11-110002-2002i−2ii3−i3i3−i3−ii−ii−33−i−iiii3i3−i3−i30000000-11−33000000000000
χ442-22-22-2-22-12-22-211-11-1-112i−2i2i−2i00−3−333-11-11000-2200−2i2ii3−i3i3−i3−ii−ii−33ii−i−i−i3−i3i3i300000001-13−3000000000000
χ452-22-22-2-22-12-22-211-11-1-11−2i2i−2i2i0033−3−3-11-110002-200−2i2ii3−i3i3−i3i−ii−i3−3ii−i−ii3i3−i3−i30000000-113−3000000000000
χ462-22-22-2-22-12-22-211-11-1-11−2i2i−2i2i0033−3−3-11-11000-22002i−2ii3−i3i3−i3i−ii−i3−3−i−iii−i3−i3i3i300000001-1−33000000000000
χ472-22-22-2-22-12-22-211-11-1-11−2i2i−2i2i00−3−333-11-110002-200−2i2i−i3i3−i3i3i−ii−i−33ii−i−i−i3−i3i3i30000000-11−33000000000000
χ482-22-22-2-22-12-22-211-11-1-11−2i2i−2i2i00−3−333-11-11000-22002i−2i−i3i3−i3i3i−ii−i−33−i−iiii3i3−i3−i300000001-13−3000000000000
χ492-2-222-22-22-222-2-2-2-22-2222-2-22000000-222-200000000000002-2-22000000000000000000000000002i−2i2i−2i000
χ502-2-222-22-22-222-2-2-2-22-2222-2-22000000-222-200000000000002-2-2200000000000000000000000000−2i2i−2i2i000
χ512-2-222-22-22-222-2-2-2-22-222-222-2000000-222-20000000000000-222-2000000000000000000000000002i−2i−2i2i000
χ522-2-222-22-22-222-2-2-2-22-222-222-2000000-222-20000000000000-222-200000000000000000000000000−2i2i2i−2i000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044-2-2-2-22222-40000000000000000220000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-42222222240000000000000000-2-20000000000000000000000000000000
χ554444-4-4-4-4400004-44-4-4-44000000000000000000022−22000000000000000022−2222−2200000000000000000000000
χ564444-4-4-4-4400004-44-4-4-440000000000000000000−22220000000000000000−2222−222200000000000000000000000
χ574444-4-4-4-4-20000-22-2222-200000023−2323−2300000000022−220000000000006−66−6−22−2200000000000000000000000
χ584444-4-4-4-4-20000-22-2222-200000023−2323−23000000000−2222000000000000−66−662−22−200000000000000000000000
χ594444-4-4-4-4-20000-22-2222-2000000−2323−232300000000022−22000000000000−66−66−22−2200000000000000000000000
χ604444-4-4-4-4-20000-22-2222-2000000−2323−2323000000000−22220000000000006−66−62−22−200000000000000000000000
χ6144-4-444-4-4-244-4-4-2-2222-220000000000-2-22204-4000000-2-2220000000000000000000000000000000000000
χ6244-4-444-4-4-244-4-4-2-2222-220000000000-2-2220-4400000022-2-20000000000000000000000000000000000000
χ6344-4-444-4-4-2-4-444-2-2222-224i4i−4i−4i00000022-2-20000000000000−2i−2i2i2i000000000000000000000000000000000
χ6444-4-444-4-4-2-4-444-2-2222-22−4i−4i4i4i00000022-2-200000000000002i2i−2i−2i000000000000000000000000000000000
χ6544-4-4-4-444400004-4-444-4-40000000000000000000000000000000000000000000000000000000000000−2i22i20
χ6644-4-4-4-444400004-4-444-4-400000000000000000000000000000000000000000000000000000000000002i2−2i20
χ674-44-44-4-444-44-44-4-44-444-40000000000-44-4400000000000000000000000000000000000000000000000000
χ684-44-44-4-44-2-44-4422-22-2-220000002323−23−232-22-200000000000000000−23230000000000000000000000000000000
χ694-44-44-4-44-2-44-4422-22-2-22000000−23−2323232-22-20000000000000000023−230000000000000000000000000000000
χ704-44-4-444-440000-4444-4-4-400004-44-4-44000000000000000000000000000000000000000000000000000000
χ714-44-4-444-440000-4444-4-4-40000-44-444-4000000000000000000000000000000000000000000000000000000
χ724-44-4-444-4-200002-2-2-222200004-4-222-200000000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000
χ734-44-4-444-4-200002-2-2-222200004-4-222-200000000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000
χ744-44-4-444-4-200002-2-2-22220000-442-2-2200000000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000
χ754-44-4-444-4-200002-2-2-22220000-442-2-2200000000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000
χ764-4-444-44-444-4-44-4-4-44-44400000000004-4-4400000000000000000000000000000000000000000000000000
χ774-4-444-44-4-24-4-44222-22-2-20000000000-222-2000000000−2i32i32i3−2i30000000000000000000000000000000000000
χ784-4-444-44-4-24-4-44222-22-2-20000000000-222-20000000002i3−2i3−2i32i30000000000000000000000000000000000000
χ794-4-444-44-4-2-444-4222-22-2-24-4-440000002-2-220000000000000-222-2000000000000000000000000000000000
χ804-4-444-44-4-2-444-4222-22-2-2-444-40000002-2-2200000000000002-2-22000000000000000000000000000000000
χ814-4-44-44-4440000-44-4-44-440000000000000000000000000000000000000000000004-400000000000000000
χ824-4-44-44-4440000-44-4-44-44000000000000000000000000000000000000000000000-4400000000000000000
χ8388-8-8-8-888-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-88-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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