Finite Group Databasebeta

← Group #10830056

Character table — Group #10830056

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order12222222344446666666444444888812121212121212124444224446666881212121212122424242424242424444488884121212124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111111-1-1111111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-111-111-1-111-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-111-1-1111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-1111-1-1-111-1-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-11111111-1-11-1-11111-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111-1-1-1-1-111-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111-1-1111-1-11111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-111-1-1-1111111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-111111-1-1-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-22222-2-2222200-200000000-2-200000000000022-2-2000000000-2000000000
χ18222222222-2-2-2-222222220000220000-2-22222-2-2-2-2-2-200-200000000-2-2000000000000-2-2220000000002000000000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222220020000000022000000000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-200200000000220000000000002222000000000-2000000000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000022222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-1-1-1-1-2-2-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-11111-1-10000-2-2-2221111-2-211-1-1-1-1-1-1-1-1111100000000-211-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-11111-1-10000-2-2-2-2-211112211-1-1-1-11111-1-1-1-1000000002-1-1110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-10000-2-22-2-2111122-1-11111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-10000-2-22221111-2-2-1-1111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-1000022-2-2-2-1-1-1-1-2-2111111-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-1000022-222-1-1-1-1221111111111-1-1-1-100000000-211-1-10000000000
χ29222-2-2-2-222-22-2222-22-2-2-22i2i−2i−2i000000-2-2000022000000000000000002i2i−2i−2i0000000000002i2i−2i−2i00000000002-2000
χ30222-2-2-2-222-22-2222-22-2-2-22i2i−2i−2i000000-2-2000022000000000000000002i2i−2i−2i000000000000−2i−2i2i2i0000000000-22000
χ31222-2-2-2-222-22-2222-22-2-2-2−2i−2i2i2i000000-2-200002200000000000000000−2i−2i2i2i0000000000002i2i−2i−2i0000000000-22000
χ32222-2-2-2-222-22-2222-22-2-2-2−2i−2i2i2i000000-2-200002200000000000000000−2i−2i2i2i000000000000−2i−2i2i2i00000000002-2000
χ3322-22-2-22-2200002-2-2-2-22200002-222−2−20022-2-2002i2i−2i−2i0000000002−200000022−2−222−2−22i−2i00−i2i2−i2i2000000000000−i2i20
χ3422-22-2-22-2200002-2-2-2-22200002-222−2−20022-2-200−2i−2i2i2i0000000002−200000022−2−222−2−2−2i2i00i2−i2i2−i2000000000000i2−i20
χ3522-22-2-22-2200002-2-2-2-22200002-2−2−2220022-2-2002i2i−2i−2i000000000−22000000−2−222−2−2222i−2i00i2−i2i2−i2000000000000i2−i20
χ3622-22-2-22-2200002-2-2-2-22200002-2−2−2220022-2-200−2i−2i2i2i000000000−22000000−2−222−2−222−2i2i00−i2i2−i2i2000000000000−i2i20
χ3722-22-2-22-2200002-2-2-2-2220000-2222−2−200-2-222002i2i−2i−2i000000000−2200000022−2−2−2−222−2i2i00−i2i2−i2i2000000000000i2−i20
χ3822-22-2-22-2200002-2-2-2-2220000-2222−2−200-2-22200−2i−2i2i2i000000000−2200000022−2−2−2−2222i−2i00i2−i2i2−i2000000000000−i2i20
χ3922-22-2-22-2200002-2-2-2-2220000-22−2−22200-2-222002i2i−2i−2i0000000002−2000000−2−22222−2−2−2i2i00i2−i2i2−i2000000000000−i2i20
χ4022-22-2-22-2200002-2-2-2-2220000-22−2−22200-2-22200−2i−2i2i2i0000000002−2000000−2−22222−2−22i−2i00−i2i2−i2i2000000000000i2−i20
χ412-2-222-2-22222-2-2-2-222-22-22i−2i2i−2i002-22-22-200002-200000002i−2i000000002i−2i2i−2i2-22-20000000000000002i−2i0000000000
χ422-2-222-2-22222-2-2-2-222-22-22i−2i2i−2i00-22-222-200002-20000000−2i2i000000002i−2i2i−2i-22-22000000000000000−2i2i0000000000
χ432-2-222-2-22222-2-2-2-222-22-2−2i2i−2i2i002-22-22-200002-20000000−2i2i00000000−2i2i−2i2i2-22-2000000000000000−2i2i0000000000
χ442-2-222-2-22222-2-2-2-222-22-2−2i2i−2i2i00-22-222-200002-200000002i−2i00000000−2i2i−2i2i-22-220000000000000002i−2i0000000000
χ452-2-222-2-22-122-2-211-1-11-112i−2i2i−2i002-22-2-113−33−3-1100000002i−2i−i3−i3i3i3003−3−ii−ii-11-113−33−3000000000−i3i3−ii0000000000
χ462-2-222-2-22-122-2-211-1-11-112i−2i2i−2i002-22-2-11−33−33-1100000002i−2ii3i3−i3−i300−33−ii−ii-11-11−33−33000000000i3−i3−ii0000000000
χ472-2-222-2-22-122-2-211-1-11-112i−2i2i−2i00-22-22-113−33−3-110000000−2i2i−i3−i3i3i3003−3−ii−ii1-11-1−33−33000000000i3−i3i−i0000000000
χ482-2-222-2-22-122-2-211-1-11-112i−2i2i−2i00-22-22-11−33−33-110000000−2i2ii3i3−i3−i300−33−ii−ii1-11-13−33−3000000000−i3i3i−i0000000000
χ492-2-222-2-22-122-2-211-1-11-11−2i2i−2i2i002-22-2-113−33−3-110000000−2i2ii3i3−i3−i3003−3i−ii−i-11-113−33−3000000000i3−i3i−i0000000000
χ502-2-222-2-22-122-2-211-1-11-11−2i2i−2i2i002-22-2-11−33−33-110000000−2i2i−i3−i3i3i300−33i−ii−i-11-11−33−33000000000−i3i3i−i0000000000
χ512-2-222-2-22-122-2-211-1-11-11−2i2i−2i2i00-22-22-113−33−3-1100000002i−2ii3i3−i3−i3003−3i−ii−i1-11-1−33−33000000000−i3i3−ii0000000000
χ522-2-222-2-22-122-2-211-1-11-11−2i2i−2i2i00-22-22-11−33−33-1100000002i−2i−i3−i3i3i300−33i−ii−i1-11-13−33−3000000000i3−i3−ii0000000000
χ532-2-2-2-222222-2-22-2-2-222-2200000000002-20000-222-22-22-20002-22-20000000000000000002-20000000000002-200000
χ542-2-2-2-222222-2-22-2-2-222-2200000000002-20000-222-22-2-22000-22-220000000000000000002-2000000000000-2200000
χ552-2-2-2-222222-2-22-2-2-222-2200000000002-20000-22-22-222-20002-22-2000000000000000000-22000000000000-2200000
χ562-2-2-2-222222-2-22-2-2-222-2200000000002-20000-22-22-22-22000-22-22000000000000000000-220000000000002-200000
χ572-2-2-2-22222-222-2-2-2-222-222-2-22000000-2200002-22-22-200000000000002-2-220000000000-2200000000002-20000000
χ582-2-2-2-22222-222-2-2-2-222-222-2-22000000-2200002-2-22-2200000000000002-2-2200000000002-20000000000-220000000
χ592-2-2-2-22222-222-2-2-2-222-22-222-2000000-2200002-22-22-20000000000000-222-20000000000-220000000000-220000000
χ602-2-2-2-22222-222-2-2-2-222-22-222-2000000-2200002-2-22-220000000000000-222-200000000002-200000000002-20000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2000044000022-2-2-2-222000000-4000000002200000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4000022222222000000400000000-2-200000000000000000000000000000000000
χ63444-4-4-4-4444-44-444-44-4-4-40000000000440000-4-40000000000000000000000000000000000000000000000000000
χ64444-4-4-4-44-24-44-4-2-22-22220000000000-2-2000022000000000−2i32i32i3−2i3000000000000000000000000000000000000000
χ65444-4-4-4-44-24-44-4-2-22-22220000000000-2-20000220000000002i3−2i3−2i32i3000000000000000000000000000000000000000
χ66444-4-4-4-44-2-44-44-2-22-22224i4i−4i−4i000000220000-2-200000000000000000−2i−2i2i2i0000000000000000000000000000000
χ67444-4-4-4-44-2-44-44-2-22-2222−4i−4i4i4i000000220000-2-2000000000000000002i2i−2i−2i0000000000000000000000000000000
χ6844-44-4-44-4-20000-22222-2-200004-42222−22−2200-2-22200000000000000022−22000000−2−222−2−22200000000000000000000000
χ6944-44-4-44-4-20000-22222-2-200004-4−22−22222200-2-222000000000000000−222200000022−2−222−2−200000000000000000000000
χ7044-44-4-44-4-20000-22222-2-20000-442222−22−220022-2-2000000000000000−2222000000−2−22222−2−200000000000000000000000
χ7144-44-4-44-4-20000-22222-2-20000-44−22−2222220022-2-200000000000000022−2200000022−2−2−2−22200000000000000000000000
χ7244-4-444-4-4400004-44-44-4-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ7344-4-444-4-4400004-44-44-4-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ744-444-44-4-440000-44-4-444-400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ754-444-44-4-440000-44-4-444-4000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ764-444-44-4-4-200002-222-2-2200000022−22−22220023−23−232300000000000000000000000−222−26−6−6600000000000000000000000
χ774-444-44-4-4-200002-222-2-2200000022−22−222200−232323−2300000000000000000000000−222−2−666−600000000000000000000000
χ784-444-44-4-4-200002-222-2-22000000−222222−220023−23−2323000000000000000000000002−2−22−666−600000000000000000000000
χ794-444-44-4-4-200002-222-2-22000000−222222−2200−232323−23000000000000000000000002−2−226−6−6600000000000000000000000
χ804-44-44-44-440000-444-4-4-440000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ814-44-44-44-440000-444-4-4-44000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ824-4-444-4-444-4-444-4-444-44-40000000000-440000-440000000000000000000000000000000000000000000000000000
χ834-4-444-4-44-2-4-44422-2-22-2200000000002-223−2323−232-2000000000000000−232300000000000000000000000000000000000
χ844-4-444-4-44-2-4-44422-2-22-2200000000002-2−2323−23232-200000000000000023−2300000000000000000000000000000000000
χ854-4-4-4-4444-24-4-44222-2-22-20000000000-2200002-200004-4000-22-22000000000000000000000000000000000000000
χ864-4-4-4-4444-24-4-44222-2-22-20000000000-2200002-20000-440002-22-2000000000000000000000000000000000000000
χ874-4-4-4-4444-2-444-4222-2-22-24-4-440000002-20000-2200000000000000000-222-20000000000000000000000000000000
χ884-4-4-4-4444-2-444-4222-2-22-2-444-40000002-20000-22000000000000000002-2-220000000000000000000000000000000
χ8988-8-888-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-88-88-8-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000000000

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