Finite Group Databasebeta

← Group #10858359

Character table — Group #10858359

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424444488884121212124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1111
χ5111111111111111111111111-1-11111111-1-1-1-111111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-111-1-11111-1-1-1-1-1-1
χ6111111111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1-111-1-111-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-111111-1-11111-1-1111-1-1-1
χ911111111111111111111-1-1-1-11111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-11111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-11-1-1-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-11111-1
χ1311111111111111111111-1-1-1-1-1-11111111-1-1-1-111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111-1-111-1-1-1-1-111-1-11
χ1411111111111111111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11-1-11111111-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-111-1-111-1-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-111-1-1-1-1111-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-2-22222-22222-20000000000-2-200000000000022-2-20000000000000-200000
χ18222222222-2-2-2-222222220000220000-2-2-22222-2-2-2-2-2-20000000000-2-2000000000000-2-2220000000000000200000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222222000000000022000000000000-2-2-2-20000000000000200000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-2200000000002200000000000022220000000000000-200000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-1-11111-10000-2-2-222-2-2-1-1-1-1111111-1-1-1-1111100000000-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-11111-10000-2-2-2-2-222-1-1-1-11111111111-1-1-1-100000000211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-100002-2-2-2-2221111-1-11111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-2-21111-1-1111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-11111-10000-222-2-2-2-2111111-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-1-11111-10000-2222222111111-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ29222-2-22-2-222-22-222-2-22-2-222-2-200000022-20000-20000000000022-2-200000000000000000022-2-2000002-200000000
χ30222-2-22-2-222-22-222-2-22-2-222-2-200000022-20000-20000000000022-2-2000000000000000000-2-22200000-2200000000
χ31222-2-22-2-222-22-222-2-22-2-2-2-22200000022-20000-200000000000-2-22200000000000000000022-2-200000-2200000000
χ32222-2-22-2-222-22-222-2-22-2-2-2-22200000022-20000-200000000000-2-222000000000000000000-2-222000002-200000000
χ3322-2-22-2-22200002-22-2-2-2200002i−2i22−2−20002i2i−2i−2i022-2-200000−i2i2000000000022−2−2−i2−i2i2i22i−2i002−22−2000000000000−i2i20
χ3422-2-22-2-22200002-22-2-2-2200002i−2i22−2−20002i2i−2i−2i0-2-22200000−i2i2000000000022−2−2−i2−i2i2i2−2i2i00−22−22000000000000i2−i20
χ3522-2-22-2-22200002-22-2-2-2200002i−2i−2−2220002i2i−2i−2i022-2-200000i2−i20000000000−2−222i2i2−i2−i22i−2i00−22−22000000000000i2−i20
χ3622-2-22-2-22200002-22-2-2-2200002i−2i−2−2220002i2i−2i−2i0-2-22200000i2−i20000000000−2−222i2i2−i2−i2−2i2i002−22−2000000000000−i2i20
χ3722-2-22-2-22200002-22-2-2-220000−2i2i22−2−2000−2i−2i2i2i022-2-200000i2−i2000000000022−2−2i2i2−i2−i2−2i2i002−22−2000000000000i2−i20
χ3822-2-22-2-22200002-22-2-2-220000−2i2i22−2−2000−2i−2i2i2i0-2-22200000i2−i2000000000022−2−2i2i2−i2−i22i−2i00−22−22000000000000−i2i20
χ3922-2-22-2-22200002-22-2-2-220000−2i2i−2−222000−2i−2i2i2i022-2-200000−i2i20000000000−2−222−i2−i2i2i2−2i2i00−22−22000000000000−i2i20
χ4022-2-22-2-22200002-22-2-2-220000−2i2i−2−222000−2i−2i2i2i0-2-22200000−i2i20000000000−2−222−i2−i2i2i22i−2i002−22−2000000000000i2−i20
χ412-2-22-22-22222-2-2-2-2222-2-200000000002-2-2000022i−2i2i−2i02i−2i00000000002i2i−2i−2i00000000002i−2i000000000000002-2000
χ422-2-22-22-22222-2-2-2-2222-2-200000000002-2-2000022i−2i2i−2i0−2i2i0000000000−2i−2i2i2i00000000002i−2i00000000000000-22000
χ432-2-22-22-22222-2-2-2-2222-2-200000000002-2-200002−2i2i−2i2i02i−2i00000000002i2i−2i−2i0000000000−2i2i00000000000000-22000
χ442-2-22-22-22222-2-2-2-2222-2-200000000002-2-200002−2i2i−2i2i0−2i2i0000000000−2i−2i2i2i0000000000−2i2i000000000000002-2000
χ452-2-22-22-222-2-222-2-2222-2-22-22-2000000-2220000-22i−2i2i−2i00000002-22-20000000000000000−2i2i000000000002i−2i000000
χ462-2-22-22-222-2-222-2-2222-2-22-22-2000000-2220000-2−2i2i−2i2i00000002-22-200000000000000002i−2i00000000000−2i2i000000
χ472-2-22-22-222-2-222-2-2222-2-2-22-22000000-2220000-22i−2i2i−2i0000000-22-220000000000000000−2i2i00000000000−2i2i000000
χ482-2-22-22-222-2-222-2-2222-2-2-22-22000000-2220000-2−2i2i−2i2i0000000-22-2200000000000000002i−2i000000000002i−2i000000
χ492-2-2-2222-22-222-2-2-2-2-22222-2-22002-22-2-22-20000200000002-2002-2-220000002-22-200000000000002-2000000000000
χ502-2-2-2222-22-222-2-2-2-2-22222-2-2200-22-22-22-2000020000000-22002-2-22000000-22-220000000000000-22000000000000
χ512-2-2-2222-22-222-2-2-2-2-2222-222-2002-22-2-22-2000020000000-2200-222-20000002-22-20000000000000-22000000000000
χ522-2-2-2222-22-222-2-2-2-2-2222-222-200-22-22-22-20000200000002-200-222-2000000-22-2200000000000002-2000000000000
χ532-2-2-2222-2-1-222-21111-1-1-12-2-22002-22-21-11−i3i3−i3i3-100000002-200-111-1−i3i3−i3i3−i3i3-11-11−i3i3−i3i3000000000-11−i3i30000000000
χ542-2-2-2222-2-1-222-21111-1-1-12-2-22002-22-21-11i3−i3i3−i3-100000002-200-111-1i3−i3i3−i3i3−i3-11-11i3−i3i3−i3000000000-11i3−i30000000000
χ552-2-2-2222-2-1-222-21111-1-1-12-2-2200-22-221-11−i3i3−i3i3-10000000-2200-111-1−i3i3−i3i3−i3i31-11-1i3−i3i3−i30000000001-1i3−i30000000000
χ562-2-2-2222-2-1-222-21111-1-1-12-2-2200-22-221-11i3−i3i3−i3-10000000-2200-111-1i3−i3i3−i3i3−i31-11-1−i3i3−i3i30000000001-1−i3i30000000000
χ572-2-2-2222-2-1-222-21111-1-1-1-222-2002-22-21-11−i3i3−i3i3-10000000-22001-1-11−i3i3i3−i3i3−i3-11-11−i3i3−i3i30000000001-1i3−i30000000000
χ582-2-2-2222-2-1-222-21111-1-1-1-222-2002-22-21-11i3−i3i3−i3-10000000-22001-1-11i3−i3−i3i3−i3i3-11-11i3−i3i3−i30000000001-1−i3i30000000000
χ592-2-2-2222-2-1-222-21111-1-1-1-222-200-22-221-11−i3i3−i3i3-100000002-2001-1-11−i3i3i3−i3i3−i31-11-1i3−i3i3−i3000000000-11−i3i30000000000
χ602-2-2-2222-2-1-222-21111-1-1-1-222-200-22-221-11i3−i3i3−i3-100000002-2001-1-11i3−i3−i3i3−i3i31-11-1−i3i3−i3i3000000000-11i3−i30000000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-20000440000222-2-2-2-220000-400000000002200000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4000022222222000040000000000-2-200000000000000000000000000000000000
χ63444-4-44-4-44-44-4444-4-44-4-40000000000-4-44000040000000000000000000000000000000000000000000000000000
χ64444-4-44-4-4-24-44-4-2-222-22244-4-4000000-2-220000200000000000-2-2220000000000000000000000000000000000000
χ65444-4-44-4-4-24-44-4-2-222-222-4-444000000-2-22000020000000000022-2-20000000000000000000000000000000000000
χ66444-4-44-4-4-2-44-44-2-222-222000000000022-20000-20000000000000000023−23−23230000000000000000000000000000000
χ67444-4-44-4-4-2-44-44-2-222-222000000000022-20000-200000000000000000−232323−230000000000000000000000000000000
χ6844-44-4-44-4400004-4-44-44-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ6944-44-4-44-4400004-4-44-44-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ7044-4-44-4-44-20000-22-2222-200004i−4i2222−22−22000−2i−2i2i2i0000000000−2i22i20000000000−2−222i2i2−i2−i200000000000000000000000
χ7144-4-44-4-44-20000-22-2222-200004i−4i−22−222222000−2i−2i2i2i00000000002i2−2i2000000000022−2−2−i2−i2i2i200000000000000000000000
χ7244-4-44-4-44-20000-22-2222-20000−4i4i2222−22−220002i2i−2i−2i00000000002i2−2i20000000000−2−222−i2−i2i2i200000000000000000000000
χ7344-4-44-4-44-20000-22-2222-20000−4i4i−22−2222220002i2i−2i−2i0000000000−2i22i2000000000022−2−2i2i2−i2−i200000000000000000000000
χ744-4444-4-4-440000-44-44-4-4400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ754-4444-4-4-440000-44-44-4-44000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ764-4444-4-4-4-200002-22-222-200000022−22−222200023−23−23230000000000000000000000−222−2−666−600000000000000000000000
χ774-4444-4-4-4-200002-22-222-200000022−22−2222000−232323−230000000000000000000000−222−26−6−6600000000000000000000000
χ784-4444-4-4-4-200002-22-222-2000000−222222−2200023−23−232300000000000000000000002−2−226−6−6600000000000000000000000
χ794-4444-4-4-4-200002-22-222-2000000−222222−22000−232323−2300000000000000000000002−2−22−666−600000000000000000000000
χ804-44-4-4-44440000-444-4-44-40000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ814-44-4-4-44440000-444-4-44-4000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ824-4-44-44-44-244-4-422-2-2-2220000000000-2220000-2000004i−4i0000000000−2i−2i2i2i0000000000000000000000000000000
χ834-4-44-44-44-244-4-422-2-2-2220000000000-2220000-200000−4i4i00000000002i2i−2i−2i0000000000000000000000000000000
χ844-4-44-44-44-2-4-44422-2-2-2224-44-40000002-2-20000200000000000-22-220000000000000000000000000000000000000
χ854-4-44-44-44-2-4-44422-2-2-222-44-440000002-2-200002000000000002-22-20000000000000000000000000000000000000
χ864-4-4-4444-444-4-44-4-4-4-444400000000004-440000-40000000000000000000000000000000000000000000000000000
χ874-4-4-4444-4-24-4-442222-2-2-20000000000-22-2−2i32i3−2i32i320000000000000002i3−2i300000000000000000000000000000000000
χ884-4-4-4444-4-24-4-442222-2-2-20000000000-22-22i3−2i32i3−2i32000000000000000−2i32i300000000000000000000000000000000000
χ8988-88-8-88-8-40000-444-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-8-888-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000000000

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