Finite Group Databasebeta

← Group #10859133

Character table — Group #10859133

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
χ31111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ51111111111111111111111-1-1-1-11111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-11
χ61111111111111111111111-1-1-1-11111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1
χ71111111111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ81111111111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ911111111111111111111-1-1111111-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-111-1-1-1-111-11111-1-1-1
χ1011111111111111111111-1-1111111-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-111-1-11-1-1-1-1111
χ1111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1111-1-111-1-111-1-1-1-1-1111
χ1211111111111111111111-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11-1-11111-1-111111-1-1-1
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-1111111-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-111-1-111-1-1-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-1111111-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-111-1-1-1-1111-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-11111-1-1-1-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-1-111-1-111111-1-111-1
χ17222222222-2-2-2-22222222220000-2-22222-2-20000-20000-2-200000000000000002222-2-2000000000-20000000
χ18222222222-2-2-2-22222222220000-2-22222-2-20000-20000-2-20000000000000000-2-2-2-22200000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-200002000022000000000000000022-2-2-2-200000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2000020000220000000000000000-2-22222000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-122-2-22-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-222222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-122-2-2-2-2-22211-1-1-1-11111-1-1-1-11111000000-2-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-2-2-222-2-211-1-1-1-111111111-1-1-1-1000000211-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-12222-222-2-2111111-1-1-1-11111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-2-222-2-2-222111111-1-1-1-1-1-1-1-11111000000211-1-1000000000000
χ2922-2-222-2-2222-2-222-2-22-2-2000000220000-2-2002-20000000000022-2-2000000002-2002-2000002-20000000000
χ3022-2-222-2-2222-2-222-2-22-2-2000000220000-2-2002-20000000000022-2-200000000-2200-2200000-220000000000
χ3122-2-222-2-2222-2-222-2-22-2-2000000220000-2-200-2200000000000-2-222000000002-2002-200000-220000000000
χ3222-2-222-2-2222-2-222-2-22-2-2000000220000-2-200-2200000000000-2-22200000000-2200-22000002-20000000000
χ3322-2-222-2-22-2-22222-2-22-2-2002i2i−2i−2i-2-2000022000000000002i2i−2i−2i0000000000002-200-2200000002i−2i00000000
χ3422-2-222-2-22-2-22222-2-22-2-2002i2i−2i−2i-2-2000022000000000002i2i−2i−2i000000000000-22002-20000000−2i2i00000000
χ3522-2-222-2-22-2-22222-2-22-2-200−2i−2i2i2i-2-200002200000000000−2i−2i2i2i0000000000002-200-220000000−2i2i00000000
χ3622-2-222-2-22-2-22222-2-22-2-200−2i−2i2i2i-2-200002200000000000−2i−2i2i2i000000000000-22002-200000002i−2i00000000
χ372-22-22-22-222-22-2-2-2-2-2222002-22-22-200002-2000000000002-22-200000000000000000000000000002i−2i2i−2i000
χ382-22-22-22-222-22-2-2-2-2-2222002-22-22-200002-2000000000002-22-20000000000000000000000000000−2i2i−2i2i000
χ392-22-22-22-222-22-2-2-2-2-222200-22-222-200002-200000000000-22-2200000000000000000000000000002i−2i−2i2i000
χ402-22-22-22-222-22-2-2-2-2-222200-22-222-200002-200000000000-22-220000000000000000000000000000−2i2i2i−2i000
χ412-2-222-2-222-222-2-2-2222-2-2002i−2i−2i2i-2200002-22-2000002i−2i002i−2i−2i2i00002i2i−2i−2i000000000002-200000000000000
χ422-2-222-2-222-222-2-2-2222-2-2002i−2i−2i2i-2200002-2-2200000−2i2i002i−2i−2i2i0000−2i−2i2i2i00000000000-2200000000000000
χ432-2-222-2-222-222-2-2-2222-2-200−2i2i2i−2i-2200002-22-200000−2i2i00−2i2i2i−2i0000−2i−2i2i2i000000000002-200000000000000
χ442-2-222-2-222-222-2-2-2222-2-200−2i2i2i−2i-2200002-2-22000002i−2i00−2i2i2i−2i00002i2i−2i−2i00000000000-2200000000000000
χ452-2-222-2-22-1-222-211-1-1-111002i−2i−2i2i1-133−3−3-112-2000002i−2i3−3−iii−i−i3i3−i3i3−i−iii−i3−i3i3i30000000-113−3000000000000
χ462-2-222-2-22-1-222-211-1-1-111002i−2i−2i2i1-133−3−3-11-2200000−2i2i3−3−iii−i−i3i3−i3i3ii−i−ii3i3−i3−i300000001-1−33000000000000
χ472-2-222-2-22-1-222-211-1-1-111002i−2i−2i2i1-1−3−333-112-2000002i−2i−33−iii−ii3−i3i3−i3−i−iiii3i3−i3−i30000000-11−33000000000000
χ482-2-222-2-22-1-222-211-1-1-111002i−2i−2i2i1-1−3−333-11-2200000−2i2i−33−iii−ii3−i3i3−i3ii−i−i−i3−i3i3i300000001-13−3000000000000
χ492-2-222-2-22-1-222-211-1-1-11100−2i2i2i−2i1-133−3−3-112-200000−2i2i3−3i−i−iii3−i3i3−i3ii−i−ii3i3−i3−i30000000-113−3000000000000
χ502-2-222-2-22-1-222-211-1-1-11100−2i2i2i−2i1-133−3−3-11-22000002i−2i3−3i−i−iii3−i3i3−i3−i−iii−i3−i3i3i300000001-1−33000000000000
χ512-2-222-2-22-1-222-211-1-1-11100−2i2i2i−2i1-1−3−333-112-200000−2i2i−33i−i−ii−i3i3−i3i3ii−i−i−i3−i3i3i30000000-11−33000000000000
χ522-2-222-2-22-1-222-211-1-1-11100−2i2i2i−2i1-1−3−333-11-22000002i−2i−33i−i−ii−i3i3−i3i3−i−iiii3i3−i3−i300000001-13−3000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022-2-2-2-2220000-4000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222000040000-2-2000000000000000000000000000000000000000
χ554444-4-4-4-4400004-4-44-44-44-40000004-44-40000000000000000000000000000000000000000000000000000
χ564444-4-4-4-4400004-4-44-44-4-44000000-44-440000000000000000000000000000000000000000000000000000
χ574444-4-4-4-4-20000-222-22-224-4000000-22-220000000000000000000006−66−66−66−600000000000000000000000
χ584444-4-4-4-4-20000-222-22-224-4000000-22-22000000000000000000000−66−66−66−6600000000000000000000000
χ594444-4-4-4-4-20000-222-22-22-440000002-22-20000000000000000000006−66−6−66−6600000000000000000000000
χ604444-4-4-4-4-20000-222-22-22-440000002-22-2000000000000000000000−66−666−66−600000000000000000000000
χ6144-4-444-4-4-244-4-4-2-222-222000000-2-2000022004-400000000000-2-2220000000000000000000000000000000
χ6244-4-444-4-4-244-4-4-2-222-222000000-2-200002200-440000000000022-2-20000000000000000000000000000000
χ6344-4-444-4-4-2-4-444-2-222-222004i4i−4i−4i220000-2-200000000000−2i−2i2i2i00000000000000000000000000000000000
χ6444-4-444-4-4-2-4-444-2-222-22200−4i−4i4i4i220000-2-2000000000002i2i−2i−2i00000000000000000000000000000000000
χ6544-4-4-4-444400004-44-4-4-4400000000000000000000000000000000000000000004i−4i0000000000000000000
χ6644-4-4-4-444400004-44-4-4-440000000000000000000000000000000000000000000−4i4i0000000000000000000
χ674-44-44-44-44-44-44-4-4-4-4444000000-440000-4400000000000000000000000000000000000000000000000000
χ684-44-44-44-4-24-44-42222-2-2-2004-44-4-220000-2200000000000-22-2200000000000000000000000000000000000
χ694-44-44-44-4-24-44-42222-2-2-200-44-44-220000-22000000000002-22-200000000000000000000000000000000000
χ704-44-44-44-4-2-44-442222-2-2-20000002-200002-2000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ714-44-44-44-4-2-44-442222-2-2-20000002-200002-20000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ724-44-4-44-4440000-444-4-44-40000000000000000000000000000000000000000000000000000000000000−2i22i20
χ734-44-4-44-4440000-444-4-44-400000000000000000000000000000000000000000000000000000000000002i2−2i20
χ744-4-444-4-4444-4-44-4-4444-4-40000004-40000-4400000000000000000000000000000000000000000000000000
χ754-4-444-4-44-24-4-4422-2-2-222000000-222323−23−232-2000000000−2323000000000000000000000000000000000000000
χ764-4-444-4-44-24-4-4422-2-2-222000000-22−23−2323232-200000000023−23000000000000000000000000000000000000000
χ774-4-44-444-440000-44-44-4-440000000000000000000−2i22i20000000000000000−2i22i22i2−2i200000000000000000000000
χ784-4-44-444-440000-44-44-4-4400000000000000000002i2−2i200000000000000002i2−2i2−2i22i200000000000000000000000
χ794-4-44-444-4-200002-22-222-20000000023−23−23230000000−2i22i2000000000000−i6i6i6−i6i2−i2−i2i200000000000000000000000
χ804-4-44-444-4-200002-22-222-20000000023−23−232300000002i2−2i2000000000000i6−i6−i6i6−i2i2i2−i200000000000000000000000
χ814-4-44-444-4-200002-22-222-200000000−232323−230000000−2i22i2000000000000i6−i6−i6i6i2−i2−i2i200000000000000000000000
χ824-4-44-444-4-200002-22-222-200000000−232323−2300000002i2−2i2000000000000−i6i6i6−i6−i2i2i2−i200000000000000000000000
χ8388-8-8-8-888-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-88-88-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000

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