Finite Group Databasebeta

← Group #10867983

Character table — Group #10867983

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order122222223444444446666666441212121212121212444444448888121212121212121212122424242424242424444444448888888812121212222444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-111111111-1-1-1-11-1-11-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111
χ91111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-11-11
χ101111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1111-11-1
χ111111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-11111-1-1-1-1111111-1-1-1-1-111-1
χ121111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1111-1-11
χ131111111111-1-1-1-11111111111-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1111-11
χ141111111111-1-1-1-11111111111-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1111-1-1-11-1
χ151111111111-1-1-1-11111111111-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-11111-1
χ161111111111-1-1-1-11111111111-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1111-1-1-1-11
χ17222222222-22222-2-2-22222222-2-2-2-22222-2-200000000000000000000-2-20000000022220000000000000000-200-200
χ18222222222-22222-2-2-22222222-2-2-2-22222-2-200000000000000000000-2-200000000-2-2-2-20000000000000000200200
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000000000000000220000000022-2-20000000000000000200-200
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000000000002200000000-2-2220000000000000000-200200
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-211111111-1-1111111110000000000000000-1-1-1-1000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000000000001111000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-100000000000000001111000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-222-2-222-2-2-1-1-1-1111111-1-1-1-111110000000000000000-1-111000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-2-2-222-2-2221111-1-1-1-1111111-1-1-1-10000000000000000-1-111000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-22222-2-2-2-222-1-1-1-11111111111-1-1-1-1000000000000000011-1-1000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-222-2-22222-2-21111-1-1-1-111-1-1-1-11111000000000000000011-1-1000000
χ2922-2-22-22-2222i2i−2i−2i-2-22-22-222-2-22i−2i2-22i2i−2i−2i2-22-22i−2i00000000000000002i−2i0000000000000000000000002-22i−2i000000
χ3022-2-22-22-2222i2i−2i−2i-2-22-22-222-2-22i−2i2-22i2i−2i−2i2-2-22−2i2i00000000000000002i−2i000000000000000000000000-22−2i2i000000
χ3122-2-22-22-222−2i−2i2i2i-2-22-22-222-2-2−2i2i2-2−2i−2i2i2i2-22-2−2i2i0000000000000000−2i2i0000000000000000000000002-2−2i2i000000
χ3222-2-22-22-222−2i−2i2i2i-2-22-22-222-2-2−2i2i2-2−2i−2i2i2i2-2-222i−2i0000000000000000−2i2i000000000000000000000000-222i−2i000000
χ3322-2-22-22-22-22i2i−2i−2i22-2-22-222-2-2−2i2i-222i2i−2i−2i-2200000000000000000000−2i2i0000000000002i2i−2i−2i00000000000002-2000
χ3422-2-22-22-22-22i2i−2i−2i22-2-22-222-2-2−2i2i-222i2i−2i−2i-2200000000000000000000−2i2i000000000000−2i−2i2i2i0000000000000-22000
χ3522-2-22-22-22-2−2i−2i2i2i22-2-22-222-2-22i−2i-22−2i−2i2i2i-22000000000000000000002i−2i0000000000002i2i−2i−2i0000000000000-22000
χ3622-2-22-22-22-2−2i−2i2i2i22-2-22-222-2-22i−2i-22−2i−2i2i2i-22000000000000000000002i−2i000000000000−2i−2i2i2i00000000000002-2000
χ3722-2-22-22-2-122i2i−2i−2i-2-221-11-1-1112i−2i-11−i−iii-112-22i−2i0000000033−3−3−i3−i3i3i3−ii33−3−3−i3−i3i3i30000000000000000-11−ii000000
χ3822-2-22-22-2-122i2i−2i−2i-2-221-11-1-1112i−2i-11−i−iii-112-22i−2i00000000−3−333i3i3−i3−i3−ii−3−333i3i3−i3−i30000000000000000-11−ii000000
χ3922-2-22-22-2-122i2i−2i−2i-2-221-11-1-1112i−2i-11−i−iii-11-22−2i2i0000000033−3−3−i3−i3i3i3−ii−3−333i3i3−i3−i300000000000000001-1i−i000000
χ4022-2-22-22-2-122i2i−2i−2i-2-221-11-1-1112i−2i-11−i−iii-11-22−2i2i00000000−3−333i3i3−i3−i3−ii33−3−3−i3−i3i3i300000000000000001-1i−i000000
χ4122-2-22-22-2-12−2i−2i2i2i-2-221-11-1-111−2i2i-11ii−i−i-112-2−2i2i0000000033−3−3i3i3−i3−i3i−i33−3−3i3i3−i3−i30000000000000000-11i−i000000
χ4222-2-22-22-2-12−2i−2i2i2i-2-221-11-1-111−2i2i-11ii−i−i-112-2−2i2i00000000−3−333−i3−i3i3i3i−i−3−333−i3−i3i3i30000000000000000-11i−i000000
χ4322-2-22-22-2-12−2i−2i2i2i-2-221-11-1-111−2i2i-11ii−i−i-11-222i−2i0000000033−3−3i3i3−i3−i3i−i−3−333−i3−i3i3i300000000000000001-1−ii000000
χ4422-2-22-22-2-12−2i−2i2i2i-2-221-11-1-111−2i2i-11ii−i−i-11-222i−2i00000000−3−333−i3−i3i3i3i−i33−3−3i3i3−i3−i300000000000000001-1−ii000000
χ452-222-2-22-2202i−2i2i−2i0002-2-22-2-2200002i−2i2i−2i00000000002−2−i2i200000000002−22−2−i2i2−i2i22-22i−2i000022−2−2−i2−i2i2i20000000000
χ462-222-2-22-2202i−2i2i−2i0002-2-22-2-2200002i−2i2i−2i00000000002−2−i2i200000000002−22−2−i2i2−i2i2-22−2i2i0000−2−222i2i2−i2−i20000000000
χ472-222-2-22-2202i−2i2i−2i0002-2-22-2-2200002i−2i2i−2i0000000000−22i2−i20000000000−22−22i2−i2i2−i22-22i−2i0000−2−222i2i2−i2−i20000000000
χ482-222-2-22-2202i−2i2i−2i0002-2-22-2-2200002i−2i2i−2i0000000000−22i2−i20000000000−22−22i2−i2i2−i2-22−2i2i000022−2−2−i2−i2i2i20000000000
χ492-222-2-22-220−2i2i−2i2i0002-2-22-2-220000−2i2i−2i2i00000000002−2i2−i200000000002−22−2i2−i2i2−i22-2−2i2i000022−2−2i2i2−i2−i20000000000
χ502-222-2-22-220−2i2i−2i2i0002-2-22-2-220000−2i2i−2i2i00000000002−2i2−i200000000002−22−2i2−i2i2−i2-222i−2i0000−2−222−i2−i2i2i20000000000
χ512-222-2-22-220−2i2i−2i2i0002-2-22-2-220000−2i2i−2i2i0000000000−22−i2i20000000000−22−22−i2i2−i2i22-2−2i2i0000−2−222−i2−i2i2i20000000000
χ522-222-2-22-220−2i2i−2i2i0002-2-22-2-220000−2i2i−2i2i0000000000−22−i2i20000000000−22−22−i2i2−i2i2-222i−2i000022−2−2i2i2−i2−i20000000000
χ532-22-222-2-22-200002-2222-2-2-22-200-2-20000220000002i−2i000000002i−2i2i−2i000000000000002i−2i2i−2i00002-22-20000000000
χ542-22-222-2-22-200002-2222-2-2-22-200-2-20000220000002i−2i000000002i−2i2i−2i00000000000000−2i2i−2i2i0000-22-220000000000
χ552-22-222-2-22-200002-2222-2-2-22-200-2-2000022000000−2i2i00000000−2i2i−2i2i000000000000002i−2i2i−2i0000-22-220000000000
χ562-22-222-2-22-200002-2222-2-2-22-200-2-2000022000000−2i2i00000000−2i2i−2i2i00000000000000−2i2i−2i2i00002-22-20000000000
χ572-2-222-2-222200002-2-2-222-2-2-22002-20000-2200002i−2i0000002i−2i2i−2i0000000000000000002-2-222i−2i2i−2i00000000000000
χ582-2-222-2-222200002-2-2-222-2-2-22002-20000-2200002i−2i0000002i−2i2i−2i000000000000000000-222-2−2i2i−2i2i00000000000000
χ592-2-222-2-222200002-2-2-222-2-2-22002-20000-220000−2i2i000000−2i2i−2i2i0000000000000000002-2-22−2i2i−2i2i00000000000000
χ602-2-222-2-222200002-2-2-222-2-2-22002-20000-220000−2i2i000000−2i2i−2i2i000000000000000000-222-22i−2i2i−2i00000000000000
χ6144444444-2-44444-4-4-4-2-2-2-2-2-2-2-4-422-2-2-2-22200000000000000000000220000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2442222222200000000000000000000-2-20000000000000000000000000000000000
χ63444-4-4-4-444000000004-44-44-4-40000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ64444-4-4-4-444000000004-44-44-4-400000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ6544-44-44-4-4400000000-4-4-4-4444000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ6644-44-44-4-4400000000-4-4-4-44440000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ6744-4-44-44-4-2-44i4i−4i−4i44-42-22-2-222−4i4i2-2−2i−2i2i2i2-2000000000000000000002i−2i0000000000000000000000000000000000
χ6844-4-44-44-4-2-4−4i−4i4i4i44-42-22-2-2224i−4i2-22i2i−2i−2i2-200000000000000000000−2i2i0000000000000000000000000000000000
χ694-444-4-44-4-204i−4i4i−4i000-222-222-20000−2i2i−2i2i000000000022−22−2i22i20000000000−22−22i2−i2i2−i200000000000000000000000000
χ704-444-4-44-4-204i−4i4i−4i000-222-222-20000−2i2i−2i2i0000000000−22222i2−2i200000000002−22−2−i2i2−i2i200000000000000000000000000
χ714-444-4-44-4-20−4i4i−4i4i000-222-222-200002i−2i2i−2i000000000022−222i2−2i20000000000−22−22−i2i2−i2i200000000000000000000000000
χ724-444-4-44-4-20−4i4i−4i4i000-222-222-200002i−2i2i−2i0000000000−2222−2i22i200000000002−22−2i2−i2i2−i200000000000000000000000000
χ734-44-444-4-4440000-44-444-4-4-44-400440000-4-400000000000000000000000000000000000000000000000000000000
χ744-44-444-4-4-240000-44-4-2-2222-2200-2-2000022000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ754-44-444-4-4-240000-44-4-2-2222-2200-2-20000220000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ764-44-444-4-4-2-400004-44-2-2222-2200220000-2-20000004i−4i00000000−2i2i−2i2i000000000000000000000000000000000000
χ774-44-444-4-4-2-400004-44-2-2222-2200220000-2-2000000−4i4i000000002i−2i2i−2i000000000000000000000000000000000000
χ784-4-444-4-444-40000-444-444-4-4-4400-4400004-400000000000000000000000000000000000000000000000000000000
χ794-4-444-4-44-2400004-4-42-2-2222-200-2200002-200004i−4i000000−2i2i−2i2i0000000000000000000000000000000000000000
χ804-4-444-4-44-2400004-4-42-2-2222-200-2200002-20000−4i4i0000002i−2i2i−2i0000000000000000000000000000000000000000
χ814-4-444-4-44-2-40000-4442-2-2222-2002-20000-22000000000000000023−23−2323000000000000000000000000000000000000
χ824-4-444-4-44-2-40000-4442-2-2222-2002-20000-220000000000000000−232323−23000000000000000000000000000000000000
χ834-4-4-4-4444404-4-44000-4-444-44-400004-4-440000000000000000000000000000000000000000000000000000000000
χ844-4-4-4-444440-444-4000-4-444-44-40000-444-40000000000000000000000000000000000000000000000000000000000
χ854-4-4-4-4444-204-4-4400022-2-22-220000-222-20000000000000000000000006−6−666−6−6600000000000000000000000000
χ864-4-4-4-4444-204-4-4400022-2-22-220000-222-2000000000000000000000000−666−6−666−600000000000000000000000000
χ874-4-4-4-4444-20-444-400022-2-22-2200002-2-220000000000000000000000006−6−66−666−600000000000000000000000000
χ884-4-4-4-4444-20-444-400022-2-22-2200002-2-22000000000000000000000000−666−66−6−6600000000000000000000000000
χ89888-8-8-8-88-400000000-44-44-444000000000000000000000000000000000000000000000000000000000000000000
χ9088-88-88-8-8-4000000004444-4-4-4000000000000000000000000000000000000000000000000000000000000000000

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