Finite Group Databasebeta

← Group #10831727

Character table — Group #10831727

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424444444412121212224444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111
χ5111111111111111111111111-1-111-1-1-1-111-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1111111-1-1-111-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1111-1-1111
χ7111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1111
χ8111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111-1-111111-1-1-1
χ911111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-11
χ1011111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1111111-1
χ1111111111111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ1211111111111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11111-1-1-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-111-1-1111-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1111-1-1-1-1-1-1-11111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111111-1-1-1-111-1
χ17222222222-2-2-2-22222222000022-2-22222-2-2-2000000000000-2-200000000000022-2-222000000000-20000000
χ18222222222-2-2-2-22222222000022-2-22222-2-2-2000000000000-2-2000000000000-2-222-2-200000000020000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-220000000000002200000000000022-2-2-2-200000000020000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2200000000000022000000000000-2-22222000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-22222-2-2-1-1-1-1111111-1-1-1-11111000000-211-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-2-2-2-2-222-1-1-1-11111111111-1-1-1-10000002-1-111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-222-2-2-2-21111-1-11111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-2-2-222221111-1-11111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-22222-2-222111111-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222-2-222-2-2111111-1-1-1-1-1-1-1-111110000002-1-111000000000000
χ29222-22-2-2-222-22-222-2-22-2-222-2-200220000-2-200000000022-2-200000000000000000000000002-2000002-2000
χ30222-22-2-2-222-22-222-2-22-2-222-2-200220000-2-200000000022-2-20000000000000000000000000-2200000-22000
χ31222-22-2-2-222-22-222-2-22-2-2-2-22200220000-2-2000000000-2-22200000000000000000000000002-200000-22000
χ32222-22-2-2-222-22-222-2-22-2-2-2-22200220000-2-2000000000-2-2220000000000000000000000000-22000002-2000
χ332-2-2222-2-22-2-222-2-2222-2-22-22-2002-200002-20002i−2i2i−2i002-22-20000002i2i−2i−2i00000000000002i−2i000000000000
χ342-2-2222-2-22-2-222-2-2222-2-22-22-2002-200002-2000−2i2i−2i2i002-22-2000000−2i−2i2i2i0000000000000−2i2i000000000000
χ352-2-2222-2-22-2-222-2-2222-2-2-22-22002-200002-20002i−2i−2i2i00-22-22000000−2i−2i2i2i00000000000002i−2i000000000000
χ362-2-2222-2-22-2-222-2-2222-2-2-22-22002-200002-2000−2i2i2i−2i00-22-220000002i2i−2i−2i0000000000000−2i2i000000000000
χ372-2-2222-2-2-1-2-22211-1-1-1112-22-200-1133−3−3-110002i−2i2i−2i00-11-113−333−3−3−i−iii−i3−i3i3i30000000−i3i3−ii000000000000
χ382-2-2222-2-2-1-2-22211-1-1-1112-22-200-1133−3−3-11000−2i2i−2i2i00-11-113−333−3−3ii−i−ii3i3−i3−i30000000i3−i3i−i000000000000
χ392-2-2222-2-2-1-2-22211-1-1-1112-22-200-11−3−333-110002i−2i2i−2i00-11-11−33−3−333−i−iiii3i3−i3−i30000000i3−i3−ii000000000000
χ402-2-2222-2-2-1-2-22211-1-1-1112-22-200-11−3−333-11000−2i2i−2i2i00-11-11−33−3−333ii−i−i−i3−i3i3i30000000−i3i3i−i000000000000
χ412-2-2222-2-2-1-2-22211-1-1-111-22-2200-1133−3−3-110002i−2i−2i2i001-11-13−3−3−333ii−i−ii3i3−i3−i30000000−i3i3−ii000000000000
χ422-2-2222-2-2-1-2-22211-1-1-111-22-2200-1133−3−3-11000−2i2i2i−2i001-11-13−3−3−333−i−iii−i3−i3i3i30000000i3−i3i−i000000000000
χ432-2-2222-2-2-1-2-22211-1-1-111-22-2200-11−3−333-110002i−2i−2i2i001-11-1−3333−3−3ii−i−i−i3−i3i3i30000000i3−i3−ii000000000000
χ442-2-2222-2-2-1-2-22211-1-1-111-22-2200-11−3−333-11000−2i2i2i−2i001-11-1−3333−3−3−i−iiii3i3−i3−i30000000−i3i3i−i000000000000
χ452-2-2-22-22222-2-22-2-2-2-2222000000-2200002-202-20000000000002-22-2000000002-22-20000000000002-200000
χ462-2-2-22-22222-2-22-2-2-2-2222000000-2200002-202-20000000000002-22-200000000-22-22000000000000-2200000
χ472-2-2-22-22222-2-22-2-2-2-2222000000-2200002-20-22000000000000-22-22000000002-22-2000000000000-2200000
χ482-2-2-22-22222-2-22-2-2-2-2222000000-2200002-20-22000000000000-22-2200000000-22-220000000000002-200000
χ492-2-2-22-2222-222-2-2-2-2-22222-2-22002-20000-220000000002-2-22000000000000002-2-220000000002-200000000
χ502-2-2-22-2222-222-2-2-2-2-22222-2-22002-20000-220000000002-2-2200000000000000-222-2000000000-2200000000
χ512-2-2-22-2222-222-2-2-2-2-2222-222-2002-20000-22000000000-222-2000000000000002-2-22000000000-2200000000
χ522-2-2-22-2222-222-2-2-2-2-2222-222-2002-20000-22000000000-222-200000000000000-222-20000000002-200000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200004422-2-2-2-222-40000000000002200000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4222222224000000000000-2-200000000000000000000000000000000000
χ55444-44-4-4-44-44-4444-4-44-4-4000000-4-400004400000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-24-44-4-2-222-22244-4-400-2-2000022000000000-2-2220000000000000000000000000000000000000
χ57444-44-4-4-4-24-44-4-2-222-222-4-44400-2-200002200000000022-2-20000000000000000000000000000000000000
χ58444-44-4-4-4-2-44-44-2-222-222000000220000-2-200000000000000023−23−23230000000000000000000000000000000
χ59444-44-4-4-4-2-44-44-2-222-222000000220000-2-2000000000000000−232323−230000000000000000000000000000000
χ6044-44-4-44-4400004-4-44-44-4000000000000000000000−2i22i200000000000000−2i22i2−2i22i200000000000000000000000
χ6144-44-4-44-4400004-4-44-44-40000000000000000000002i2−2i2000000000000002i2−2i22i2−2i200000000000000000000000
χ6244-44-4-44-4-20000-222-22-2200000000−2i32i3−2i32i3000000000−2i22i200000000006−66−6i2−i2i2−i200000000000000000000000
χ6344-44-4-44-4-20000-222-22-2200000000−2i32i3−2i32i30000000002i2−2i20000000000−66−66−i2i2−i2i200000000000000000000000
χ6444-44-4-44-4-20000-222-22-22000000002i3−2i32i3−2i3000000000−2i22i20000000000−66−66i2−i2i2−i200000000000000000000000
χ6544-44-4-44-4-20000-222-22-22000000002i3−2i32i3−2i30000000002i2−2i200000000006−66−6−i2i2−i2i200000000000000000000000
χ6644-4-4-44-44400004-44-4-4-440000000000000000000000000000000000000000000004i−4i00000000000000000
χ6744-4-4-44-44400004-44-4-4-44000000000000000000000000000000000000000000000−4i4i00000000000000000
χ684-444-4-4-4440000-44-44-4-4400004i−4i004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ694-444-4-4-4440000-44-44-4-440000−4i4i00−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ704-444-4-4-44-200002-22-222-200004i−4i00−2i2i2i−2i000000000000000000000i6−i6−i6i6−666−600000000000000000000000
χ714-444-4-4-44-200002-22-222-200004i−4i00−2i2i2i−2i000000000000000000000−i6i6i6−i66−6−6600000000000000000000000
χ724-444-4-4-44-200002-22-222-20000−4i4i002i−2i−2i2i000000000000000000000i6−i6−i6i66−6−6600000000000000000000000
χ734-444-4-4-44-200002-22-222-20000−4i4i002i−2i−2i2i000000000000000000000−i6i6i6−i6−666−600000000000000000000000
χ744-44-4-444-440000-444-4-44-40000000000000000000000000000000000000000000000000000000000000−2i22i20
χ754-44-4-444-440000-444-4-44-400000000000000000000000000000000000000000000000000000000000002i2−2i20
χ764-4-4444-4-4444-4-4-4-4444-4-4000000-440000-4400000000000000000000000000000000000000000000000000
χ774-4-4444-4-4-244-4-422-2-2-2220000002-22323−23−232-20000000000000−232300000000000000000000000000000000000
χ784-4-4444-4-4-244-4-422-2-2-2220000002-2−23−2323232-2000000000000023−2300000000000000000000000000000000000
χ794-4-4-44-444-24-4-442222-2-2-20000002-20000-2204-4000000000000-22-220000000000000000000000000000000
χ804-4-4-44-444-24-4-442222-2-2-20000002-20000-220-440000000000002-22-20000000000000000000000000000000
χ814-4-4-44-444-2-444-42222-2-2-24-4-4400-2200002-2000000000-222-20000000000000000000000000000000000000
χ824-4-4-44-444-2-444-42222-2-2-2-444-400-2200002-20000000002-2-220000000000000000000000000000000000000
χ8388-8-8-88-88-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-888-8-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000

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