Finite Group Databasebeta

← Group #10830064

Character table — Group #10830064

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424444488884121212122244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-11-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-111-1-111-1
χ911111111111111111111-1-111111111-1-1-1-111111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-111-1-1-11111-1-1-1
χ1011111111111111111111-1-111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-1111
χ1111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-1-111-1-1111
χ1211111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111111111-1-1111-1-111-1-1-1
χ1311111111111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111111-1-111-1-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111-1-1-1-11111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-111-1-1111-1-1-1-11
χ17222222222-2-2-2-2222222222000000002222-2-2-2-22222-20000000000-2-2000000000000-2-22200000000000-20000000
χ18222222222-2-2-2-2222222222000000002222-2-2-2-2-2-2-2-2-20000000000-2-200000000000022-2-20000000000020000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222222000000000022000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-22000000000022000000000000222200000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100002222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-100002-2-2-2-2221111-1-11111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-21111-1-1111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2222222221111-1-1-1-10000-222-2-2-2-2111111-1-1-1-1-1-1-1-1111100000000-211-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-21111-1-1-1-10000-2-2-2-2-222111111-1-1-1-11111-1-1-1-1000000002-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-10000-2-2-222-2-2-1-1-1-1111111-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-21111-1-1-1-10000-2222222-1-1-1-11111111111-1-1-1-100000000-211-1-10000000000
χ29222-2-2-2-222-22-2222-2-2-22-2002i2i−2i−2i00000000-2-222000000000000000002i2i−2i−2i0000000000002i2i−2i−2i00000000002-2000
χ30222-2-2-2-222-22-2222-2-2-22-2002i2i−2i−2i00000000-2-222000000000000000002i2i−2i−2i000000000000−2i−2i2i2i0000000000-22000
χ31222-2-2-2-222-22-2222-2-2-22-200−2i−2i2i2i00000000-2-22200000000000000000−2i−2i2i2i0000000000002i2i−2i−2i0000000000-22000
χ32222-2-2-2-222-22-2222-2-2-22-200−2i−2i2i2i00000000-2-22200000000000000000−2i−2i2i2i000000000000−2i−2i2i2i00000000002-2000
χ3322-2-22-22-2200002-22-2-2-222i−2i000022−2−22i2i−2i−2i00002i2i−2i−2i00000−i2i2000000000022−2−2−i2−i2i2i2002-2−i2i2−i2i20000000000002−20
χ3422-2-22-22-2200002-22-2-2-222i−2i000022−2−22i2i−2i−2i0000−2i−2i2i2i00000−i2i2000000000022−2−2−i2−i2i2i200-22i2−i2i2−i2000000000000−220
χ3522-2-22-22-2200002-22-2-2-222i−2i0000−2−2222i2i−2i−2i00002i2i−2i−2i00000i2−i20000000000−2−222i2i2−i2−i2002-2i2−i2i2−i2000000000000−220
χ3622-2-22-22-2200002-22-2-2-222i−2i0000−2−2222i2i−2i−2i0000−2i−2i2i2i00000i2−i20000000000−2−222i2i2−i2−i200-22−i2i2−i2i20000000000002−20
χ3722-2-22-22-2200002-22-2-2-22−2i2i000022−2−2−2i−2i2i2i00002i2i−2i−2i00000i2−i2000000000022−2−2i2i2−i2−i200-22−i2i2−i2i2000000000000−220
χ3822-2-22-22-2200002-22-2-2-22−2i2i000022−2−2−2i−2i2i2i0000−2i−2i2i2i00000i2−i2000000000022−2−2i2i2−i2−i2002-2i2−i2i2−i20000000000002−20
χ3922-2-22-22-2200002-22-2-2-22−2i2i0000−2−222−2i−2i2i2i00002i2i−2i−2i00000−i2i20000000000−2−222−i2−i2i2i200-22i2−i2i2−i20000000000002−20
χ4022-2-22-22-2200002-22-2-2-22−2i2i0000−2−222−2i−2i2i2i0000−2i−2i2i2i00000−i2i20000000000−2−222−i2−i2i2i2002-2−i2i2−i2i2000000000000−220
χ412-2-222-2-22222-2-2-2-22-222-2002i−2i2i−2i2-22-200002-22-2000002i−2i00000000002i−2i2i−2i2-22-20000000000000002i−2i0000000000
χ422-2-222-2-22222-2-2-2-22-222-2002i−2i2i−2i-22-2200002-22-200000−2i2i00000000002i−2i2i−2i-22-22000000000000000−2i2i0000000000
χ432-2-222-2-22222-2-2-2-22-222-200−2i2i−2i2i2-22-200002-22-200000−2i2i0000000000−2i2i−2i2i2-22-2000000000000000−2i2i0000000000
χ442-2-222-2-22222-2-2-2-22-222-200−2i2i−2i2i-22-2200002-22-2000002i−2i0000000000−2i2i−2i2i-22-220000000000000002i−2i0000000000
χ452-2-222-2-22-122-2-211-11-1-11002i−2i2i−2i2-22-23−33−3-11-11000002i−2i0000−i3−i3i3i33−3−ii−ii-11-113−33−3000000000−i3i3−ii0000000000
χ462-2-222-2-22-122-2-211-11-1-11002i−2i2i−2i2-22-2−33−33-11-11000002i−2i0000i3i3−i3−i3−33−ii−ii-11-11−33−33000000000i3−i3−ii0000000000
χ472-2-222-2-22-122-2-211-11-1-11002i−2i2i−2i-22-223−33−3-11-1100000−2i2i0000−i3−i3i3i33−3−ii−ii1-11-1−33−33000000000i3−i3i−i0000000000
χ482-2-222-2-22-122-2-211-11-1-11002i−2i2i−2i-22-22−33−33-11-1100000−2i2i0000i3i3−i3−i3−33−ii−ii1-11-13−33−3000000000−i3i3i−i0000000000
χ492-2-222-2-22-122-2-211-11-1-1100−2i2i−2i2i2-22-23−33−3-11-1100000−2i2i0000i3i3−i3−i33−3i−ii−i-11-113−33−3000000000i3−i3i−i0000000000
χ502-2-222-2-22-122-2-211-11-1-1100−2i2i−2i2i2-22-2−33−33-11-1100000−2i2i0000−i3−i3i3i3−33i−ii−i-11-11−33−33000000000−i3i3i−i0000000000
χ512-2-222-2-22-122-2-211-11-1-1100−2i2i−2i2i-22-223−33−3-11-11000002i−2i0000i3i3−i3−i33−3i−ii−i1-11-1−33−33000000000−i3i3−ii0000000000
χ522-2-222-2-22-122-2-211-11-1-1100−2i2i−2i2i-22-22−33−33-11-11000002i−2i0000−i3−i3i3i3−33i−ii−i1-11-13−33−3000000000i3−i3−ii0000000000
χ532-2-2-2-222222-2-22-2-2-22-222000000000000002-2-222-22-20002-2002-22-2000000000000002-2000000000002-200000000
χ542-2-2-2-222222-2-22-2-2-22-222000000000000002-2-222-22-2000-2200-22-22000000000000002-200000000000-2200000000
χ552-2-2-2-222222-2-22-2-2-22-222000000000000002-2-22-22-220002-2002-22-200000000000000-2200000000000-2200000000
χ562-2-2-2-222222-2-22-2-2-22-222000000000000002-2-22-22-22000-2200-22-2200000000000000-22000000000002-200000000
χ572-2-2-2-22222-222-2-2-2-22-222002-2-2200000000-222-22-22-200000000000002-2-2200000000-22000000000000002-200000
χ582-2-2-2-22222-222-2-2-2-22-222002-2-2200000000-222-2-22-2200000000000002-2-22000000002-200000000000000-2200000
χ592-2-2-2-22222-222-2-2-2-22-22200-222-200000000-222-22-22-20000000000000-222-200000000-2200000000000000-2200000
χ602-2-2-2-22222-222-2-2-2-22-22200-222-200000000-222-2-22-220000000000000-222-2000000002-2000000000000002-200000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-24400000000-2-2-2-222220000-400000000002200000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-40000000022222222000040000000000-2-200000000000000000000000000000000000
χ63444-4-4-4-4444-44-444-4-4-44-40000000000000044-4-40000000000000000000000000000000000000000000000000000
χ64444-4-4-4-44-24-44-4-2-2222-2200000000000000-2-22200000000000−2i32i32i3−2i30000000000000000000000000000000000000
χ65444-4-4-4-44-24-44-4-2-2222-2200000000000000-2-222000000000002i3−2i3−2i32i30000000000000000000000000000000000000
χ66444-4-4-4-44-2-44-44-2-2222-22004i4i−4i−4i0000000022-2-200000000000000000−2i−2i2i2i0000000000000000000000000000000
χ67444-4-4-4-44-2-44-44-2-2222-2200−4i−4i4i4i0000000022-2-2000000000000000002i2i−2i−2i0000000000000000000000000000000
χ6844-44-44-4-4400004-4-444-4-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ6944-44-44-4-4400004-4-444-4-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ7044-4-44-44-4-20000-22-2222-24i−4i00002222−22−22−2i−2i2i2i0000000000000−2i22i20000000000−2−222i2i2−i2−i200000000000000000000000
χ7144-4-44-44-4-20000-22-2222-24i−4i0000−22−222222−2i−2i2i2i00000000000002i2−2i2000000000022−2−2−i2−i2i2i200000000000000000000000
χ7244-4-44-44-4-20000-22-2222-2−4i4i00002222−22−222i2i−2i−2i00000000000002i2−2i20000000000−2−222−i2−i2i2i200000000000000000000000
χ7344-4-44-44-4-20000-22-2222-2−4i4i0000−22−2222222i2i−2i−2i0000000000000−2i22i2000000000022−2−2i2i2−i2−i200000000000000000000000
χ744-444-4-44-440000-44-4-44-440000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ754-444-4-44-440000-44-4-44-44000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ764-44-444-4-440000-4444-4-4-400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ774-44-444-4-440000-4444-4-4-4000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ784-44-444-4-4-200002-2-2-222200000022−22−2222−2i32i32i3−2i30000000000000000000000000−222−2i6−i6−i6i600000000000000000000000
χ794-44-444-4-4-200002-2-2-222200000022−22−22222i3−2i3−2i32i30000000000000000000000000−222−2−i6i6i6−i600000000000000000000000
χ804-44-444-4-4-200002-2-2-2222000000−222222−22−2i32i32i3−2i300000000000000000000000002−2−22−i6i6i6−i600000000000000000000000
χ814-44-444-4-4-200002-2-2-2222000000−222222−222i3−2i3−2i32i300000000000000000000000002−2−22i6−i6−i6i600000000000000000000000
χ824-4-444-4-444-4-444-4-44-444-400000000000000-44-440000000000000000000000000000000000000000000000000000
χ834-4-444-4-44-2-4-44422-22-2-22000000000023−2323−232-22-2000000000000000−232300000000000000000000000000000000000
χ844-4-444-4-44-2-4-44422-22-2-220000000000−2323−23232-22-200000000000000023−2300000000000000000000000000000000000
χ854-4-4-4-4444-24-4-44222-22-2-200000000000000-222-200000004-400-22-220000000000000000000000000000000000000
χ864-4-4-4-4444-24-4-44222-22-2-200000000000000-222-20000000-44002-22-20000000000000000000000000000000000000
χ874-4-4-4-4444-2-444-4222-22-2-2004-4-44000000002-2-2200000000000000000-222-20000000000000000000000000000000
χ884-4-4-4-4444-2-444-4222-22-2-200-444-4000000002-2-22000000000000000002-2-220000000000000000000000000000000
χ8988-88-88-8-8-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-888-8-88-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000

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