Finite Group Databasebeta

← Group #10858314

Character table — Group #10858314

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order12222222344446666666222244888812121212121212124444444446666881212121212122424242424242424444488884121212122244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1111
χ5111111111111111111111111-1-11111111-1-1-1-111111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-111-1-111-1-1-111-1-1-1
χ6111111111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1111-1-1111
χ7111111111111111111111111-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-1-111111
χ8111111111111111111111111-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-11111111-1-1-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1
χ1311111111111111111111-1-1-1-1-1-11111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111111-1-111-1-1-111-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-11-1-111111-1-11111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-111-111-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-111-111-1-1-1-1111111-1-1-1-1-1-11111-1-1111111-111-1-1-1-11-1-111-1-11
χ17222222222-2-2-2-222222220000220000-2-2-22222-2222200-2000000000000-2-200000000-2-22200000000000-20000000
χ18222222222-2-2-2-222222220000220000-2-2-22222-2-2-2-2-200-2000000000000-2-20000000022-2-20000000000020000000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222220020000000000002200000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-20020000000000002200000000222200000000000-20000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-1-11111-10000-2-2-222-1-1-1-1-2-2111111-1-1-1-1111100000000-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-11111-10000-2-2-2-2-2-1-1-1-1221111111111-1-1-1-100000000211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-10000-2-22-2-21111221111-1-1-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-10000-2-22221111-2-21111-1-111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-11111-1000022-2-2-21111-2-2-1-1-1-111-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-1-11111-1000022-222111122-1-1-1-1111111-1-1-1-100000000-2-1-1110000000000
χ292222-2-2-2-222-22-222-2-22-2-222-2-200000022-20000-200000000022-2-20000000000000000000022-2-2000002-200000000
χ302222-2-2-2-222-22-222-2-22-2-222-2-200000022-20000-200000000022-2-200000000000000000000-2-22200000-2200000000
χ312222-2-2-2-222-22-222-2-22-2-2-2-22200000022-20000-2000000000-2-2220000000000000000000022-2-200000-2200000000
χ322222-2-2-2-222-22-222-2-22-2-2-2-22200000022-20000-2000000000-2-22200000000000000000000-2-222000002-200000000
χ3322-2-222-2-2200002-22-2-22-200002-2−i2−i2i2i200022-2-202i2i−2i−2i000000000−i2i2000000−i2−i2i2i2−i2−i2i2i2002i−2i2−22−20000000000002−20
χ3422-2-222-2-2200002-22-2-22-200002-2−i2−i2i2i200022-2-20−2i−2i2i2i000000000−i2i2000000−i2−i2i2i2−i2−i2i2i200−2i2i−22−22000000000000−220
χ3522-2-222-2-2200002-22-2-22-200002-2i2i2−i2−i200022-2-202i2i−2i−2i000000000i2−i2000000i2i2−i2−i2i2i2−i2−i2002i−2i−22−22000000000000−220
χ3622-2-222-2-2200002-22-2-22-200002-2i2i2−i2−i200022-2-20−2i−2i2i2i000000000i2−i2000000i2i2−i2−i2i2i2−i2−i200−2i2i2−22−20000000000002−20
χ3722-2-222-2-2200002-22-2-22-20000-22−i2−i2i2i2000-2-22202i2i−2i−2i000000000i2−i2000000−i2−i2i2i2i2i2−i2−i200−2i2i2−22−2000000000000−220
χ3822-2-222-2-2200002-22-2-22-20000-22−i2−i2i2i2000-2-2220−2i−2i2i2i000000000i2−i2000000−i2−i2i2i2i2i2−i2−i2002i−2i−22−220000000000002−20
χ3922-2-222-2-2200002-22-2-22-20000-22i2i2−i2−i2000-2-22202i2i−2i−2i000000000−i2i2000000i2i2−i2−i2−i2−i2i2i200−2i2i−22−220000000000002−20
χ4022-2-222-2-2200002-22-2-22-20000-22i2i2−i2−i2000-2-2220−2i−2i2i2i000000000−i2i2000000i2i2−i2−i2−i2−i2i2i2002i−2i2−22−2000000000000−220
χ412-2-222-2-222-222-2-2-2-2-22222-22-2002-22-22-2-20000200000002-22-22-2000000002-22-200000000000002-2000000000000
χ422-2-222-2-222-222-2-2-2-2-22222-22-200-22-222-2-2000020000000-222-22-200000000-22-220000000000000-22000000000000
χ432-2-222-2-222-222-2-2-2-2-2222-22-22002-22-22-2-2000020000000-22-22-22000000002-22-20000000000000-22000000000000
χ442-2-222-2-222-222-2-2-2-2-2222-22-2200-22-222-2-20000200000002-2-22-2200000000-22-2200000000000002-2000000000000
χ452-2-222-2-22-1-222-21111-1-1-12-22-2002-22-2-111−i3i3−i3i3-100000002-2-11-1100−i3−i3i3i3−i3i3-11-11−i3i3−i3i3000000000-11−i3i30000000000
χ462-2-222-2-22-1-222-21111-1-1-12-22-2002-22-2-111i3−i3i3−i3-100000002-2-11-1100i3i3−i3−i3i3−i3-11-11i3−i3i3−i3000000000-11i3−i30000000000
χ472-2-222-2-22-1-222-21111-1-1-12-22-200-22-22-111−i3i3−i3i3-10000000-22-11-1100−i3−i3i3i3−i3i31-11-1i3−i3i3−i30000000001-1i3−i30000000000
χ482-2-222-2-22-1-222-21111-1-1-12-22-200-22-22-111i3−i3i3−i3-10000000-22-11-1100i3i3−i3−i3i3−i31-11-1−i3i3−i3i30000000001-1−i3i30000000000
χ492-2-222-2-22-1-222-21111-1-1-1-22-22002-22-2-111−i3i3−i3i3-10000000-221-11-100i3i3−i3−i3−i3i3-11-11−i3i3−i3i30000000001-1i3−i30000000000
χ502-2-222-2-22-1-222-21111-1-1-1-22-22002-22-2-111i3−i3i3−i3-10000000-221-11-100−i3−i3i3i3i3−i3-11-11i3−i3i3−i30000000001-1−i3i30000000000
χ512-2-222-2-22-1-222-21111-1-1-1-22-2200-22-22-111−i3i3−i3i3-100000002-21-11-100i3i3−i3−i3−i3i31-11-1i3−i3i3−i3000000000-11−i3i30000000000
χ522-2-222-2-22-1-222-21111-1-1-1-22-2200-22-22-111i3−i3i3−i3-100000002-21-11-100−i3−i3i3i3i3−i31-11-1−i3i3−i3i3000000000-11i3−i30000000000
χ532-2-22-222-2222-2-2-2-2222-2-20000000000-22-2000022i−2i2i−2i2i−2i0000000002i−2i2i−2i00000000002i−2i000000000000002-200000
χ542-2-22-222-2222-2-2-2-2222-2-20000000000-22-2000022i−2i2i−2i−2i2i000000000−2i2i−2i2i00000000002i−2i00000000000000-2200000
χ552-2-22-222-2222-2-2-2-2222-2-20000000000-22-200002−2i2i−2i2i2i−2i0000000002i−2i2i−2i0000000000−2i2i00000000000000-2200000
χ562-2-22-222-2222-2-2-2-2222-2-20000000000-22-200002−2i2i−2i2i−2i2i000000000−2i2i−2i2i0000000000−2i2i000000000000002-200000
χ572-2-22-222-22-2-222-2-2222-2-22-2-220000002-220000-22i−2i2i−2i000002-2-220000000000000000−2i2i00000000000000002i−2i000
χ582-2-22-222-22-2-222-2-2222-2-22-2-220000002-220000-2−2i2i−2i2i000002-2-2200000000000000002i−2i0000000000000000−2i2i000
χ592-2-22-222-22-2-222-2-2222-2-2-222-20000002-220000-22i−2i2i−2i00000-222-20000000000000000−2i2i0000000000000000−2i2i000
χ602-2-22-222-22-2-222-2-2222-2-2-222-20000002-220000-2−2i2i−2i2i00000-222-200000000000000002i−2i00000000000000002i−2i000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-20000440000222-2-2-2-22000000-4000000000000220000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-40000222222220000004000000000000-2-20000000000000000000000000000000
χ634444-4-4-4-44-44-4444-4-44-4-40000000000-4-44000040000000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-24-44-4-2-222-22244-4-4000000-2-2200002000000000-2-222000000000000000000000000000000000000000
χ654444-4-4-4-4-24-44-4-2-222-222-4-444000000-2-220000200000000022-2-2000000000000000000000000000000000000000
χ664444-4-4-4-4-2-44-44-2-222-222000000000022-20000-200000000000000023−23−2323000000000000000000000000000000000
χ674444-4-4-4-4-2-44-44-2-222-222000000000022-20000-2000000000000000−232323−23000000000000000000000000000000000
χ6844-4-444-4-4-20000-22-222-2200004-4−2i2−2i22i22i2000-2-22200000000000000−2i22i2000000i2i2−i2−i2i2i2−i2−i200000000000000000000000
χ6944-4-444-4-4-20000-22-222-2200004-42i22i2−2i2−2i2000-2-222000000000000002i2−2i2000000−i2−i2i2i2−i2−i2i2i200000000000000000000000
χ7044-4-444-4-4-20000-22-222-220000-44−2i2−2i22i22i200022-2-2000000000000002i2−2i2000000i2i2−i2−i2−i2−i2i2i200000000000000000000000
χ7144-4-444-4-4-20000-22-222-220000-442i22i2−2i2−2i200022-2-200000000000000−2i22i2000000−i2−i2i2i2i2i2−i2−i200000000000000000000000
χ7244-4-4-4-444400004-4-44-4-4400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ7344-4-4-4-444400004-4-44-4-44000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ744-44-44-44-440000-44-44-44-4000000−2i22i22i2−2i200000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ754-44-44-44-440000-44-44-44-40000002i2−2i2−2i22i2000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ764-44-44-44-4-200002-22-22-22000000−2i22i22i2−2i2000−2i32i32i3−2i30000000000000000000000i2−i2−i2i2−666−600000000000000000000000
χ774-44-44-44-4-200002-22-22-22000000−2i22i22i2−2i20002i3−2i3−2i32i30000000000000000000000i2−i2−i2i26−6−6600000000000000000000000
χ784-44-44-44-4-200002-22-22-220000002i2−2i2−2i22i2000−2i32i32i3−2i30000000000000000000000−i2i2i2−i26−6−6600000000000000000000000
χ794-44-44-44-4-200002-22-22-220000002i2−2i2−2i22i20002i3−2i3−2i32i30000000000000000000000−i2i2i2−i2−666−600000000000000000000000
χ804-44-4-44-4440000-444-4-4-440000000000000000004-4-44000000000000000000000000000000000000000000000000
χ814-44-4-44-4440000-444-4-4-44000000000000000000-444-4000000000000000000000000000000000000000000000000
χ824-4-444-4-4444-4-44-4-4-4-44440000000000-4440000-40000000000000000000000000000000000000000000000000000
χ834-4-444-4-44-24-4-442222-2-2-200000000002-2-2−2i32i3−2i32i3200000000000000000002i3−2i30000000000000000000000000000000
χ844-4-444-4-44-24-4-442222-2-2-200000000002-2-22i3−2i32i3−2i320000000000000000000−2i32i30000000000000000000000000000000
χ854-4-44-444-4-244-4-422-2-2-22200000000002-220000-200004i−4i000000000−2i2i−2i2i000000000000000000000000000000000
χ864-4-44-444-4-244-4-422-2-2-22200000000002-220000-20000−4i4i0000000002i−2i2i−2i000000000000000000000000000000000
χ874-4-44-444-4-2-4-44422-2-2-2224-4-44000000-22-200002000000000-222-2000000000000000000000000000000000000000
χ884-4-44-444-4-2-4-44422-2-2-222-444-4000000-22-2000020000000002-2-22000000000000000000000000000000000000000
χ8988-8-8-8-888-40000-444-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-88-88-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000000000

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