Finite Group Databasebeta

← Group #10828731

Character table — Group #10828731

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222224444444444444444444444444888888888888888888888888888888882424242424242424242424244848
order122222344444466622444446666121212121212121212121212121224444444446661212121212121212121212121212121212121244444444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-11-11-1-1-11-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111-1-1-1-11-11-1-1-11-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-11-11-1-1111-1-1111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ61111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-11-11-1-1111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-11-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ81111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ911111111-1-1111111-1-1-1111111-1-111111111-1-1111111-1-1-1-1-1-111-111-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ1011111111-1-1111111-1-1-1111111-1-111111111-1-1111111-1-1-1-1-1-111-111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-11
χ1111111111-1-1111111-1-1-1111111-1-111111111-1-11111-1-111-11-11-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-11
χ1211111111-1-1111111-1-1-1111111-1-111111111-1-11111-1-111-11-11-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1111-1
χ1311111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111-11-1-1-1-11111-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1
χ1411111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111-11-1-1-1-11111-1-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-1-11
χ1511111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-111-1-1111111-1-1-1-111-1-111-1-1-1-111-11
χ1611111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-111-1-1111111-1-1-1-1-1-111-1-11111-1-11-1
χ172222222-222-2-2-2222-2-22000022-2-20000-2-2-2-2220000002-200002-2-2000000200000022-2-222-2-200000000000000
χ182222222-222-2-2-2222-2-22000022-2-20000-2-2-2-222000000-220000-22-20000002000000-2-222-2-22200000000000000
χ192222222-2-2-2-2-2-222222-2000022220000-2-2-2-2-2-20000002-20000-222000000-2000000-2-22222-2-200000000000000
χ202222222-2-2-2-2-2-222222-2000022220000-2-2-2-2-2-2000000-2200002-22000000-200000022-2-2-2-22200000000000000
χ21222222-1222222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ22222222-1222222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22-22-2-2-2-111-1-111-1-1-111111111111100000000000000
χ23222222-1222222-1-1-1222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1111122-2-2-22-22-2-2-1-1-111-1-1-111-1-1-1-11111111100000000000000
χ24222222-1222222-1-1-1222-2-2-2-2-1-1-1-11111-1-1-1-1-1-11111-2-222-2-2-2-222-1111111-1111111-1-1-1-1-1-1-1-100000000000000
χ25222222-12-2-2222-1-1-1-2-2-22222-1-111-1-1-1-1-1-1-1-111-1-1-1-122-2-2-2-2-2-2221-1-11111111-1-111-1-1-1-1111100000000000000
χ26222222-12-2-2222-1-1-1-2-2-22222-1-111-1-1-1-1-1-1-1-111-1-1-1-1-2-222-22-22-2-211111-1-111111-1-11111-1-1-1-100000000000000
χ27222222-12-2-2222-1-1-1-2-2-2-2-2-2-2-1-1111111-1-1-1-111111122222-22-2-2-21-1-1-1-1111-1-1-1-1111111-1-1-1-100000000000000
χ28222222-12-2-2222-1-1-1-2-2-2-2-2-2-2-1-1111111-1-1-1-1111111-2-2-2-2222222111-1-1-1-11-1-111-1-1-1-1-1-1111100000000000000
χ29222222-1-222-2-2-2-1-1-1-2-220000-1-111−i3−i3i3i31111-1-1−i3−i3i3i3002-200002-21−i3i3−i3i3−i3i3-1−i3i3−i3i3−i3i3-1-111-1-11100000000000000
χ30222222-1-222-2-2-2-1-1-1-2-220000-1-111−i3−i3i3i31111-1-1−i3−i3i3i300-220000-221i3−i3−i3i3i3−i3-1−i3i3i3−i3i3−i311-1-111-1-100000000000000
χ31222222-1-222-2-2-2-1-1-1-2-220000-1-111i3i3−i3−i31111-1-1i3i3−i3−i3002-200002-21i3−i3i3−i3i3−i3-1i3−i3i3−i3i3−i3-1-111-1-11100000000000000
χ32222222-1-222-2-2-2-1-1-1-2-220000-1-111i3i3−i3−i31111-1-1i3i3−i3−i300-220000-221−i3i3i3−i3−i3i3-1i3−i3−i3i3−i3i311-1-111-1-100000000000000
χ33222222-1-2-2-2-2-2-2-1-1-122-20000-1-1-1-1−i3−i3i3i3111111−i3−i3i3i3002-20000-22-1i3−i3i3−i3−i3i31i3−i3i3−i3−i3i311-1-1-1-11100000000000000
χ34222222-1-2-2-2-2-2-2-1-1-122-20000-1-1-1-1−i3−i3i3i3111111−i3−i3i3i300-2200002-2-1−i3i3i3−i3i3−i31i3−i3−i3i3i3−i3-1-11111-1-100000000000000
χ35222222-1-2-2-2-2-2-2-1-1-122-20000-1-1-1-1i3i3−i3−i3111111i3i3−i3−i3002-20000-22-1−i3i3−i3i3i3−i31−i3i3−i3i3i3−i311-1-1-1-11100000000000000
χ36222222-1-2-2-2-2-2-2-1-1-122-20000-1-1-1-1i3i3−i3−i3111111i3i3−i3−i300-2200002-2-1i3−i3−i3i3−i3i31−i3i3i3−i3−i3i3-1-11111-1-100000000000000
χ372222-2-22222-2-222222-2-222-2-2-2-2-2-2222222-2-222-2-2-2-20000-202000200-2-200-22200000000000000000000000000
χ382222-2-22222-2-222222-2-2-2-222-2-2-2-2-2-2-2-222-2-2222222000020-20002002200-2-2-200000000000000000000000000
χ392222-2-222-2-2-2-22222-22222-2-2-2-222222222-2-2-2-2-2-2-2-2000020-2000-20022002-2-200000000000000000000000000
χ402222-2-222-2-2-2-22222-222-2-222-2-222-2-2-2-222-2-2-2-222220000-202000-200-2-20022200000000000000000000000000
χ412222-2-22-22222-2222-22-20000-2-2220000-2-2222200002-200020-200-2220022-200-2-2-2-20000000000000000000000
χ422222-2-22-22222-2222-22-20000-2-2220000-2-222220000-22000-20200-2-2-200-2-2-20022220000000000000000000000
χ432222-2-22-2-2-222-22222-220000-2-2-2-20000-2-222-2-200002-2000-2020022200-2-2200-2-2220000000000000000000000
χ442222-2-22-2-2-222-22222-220000-2-2-2-20000-2-222-2-20000-2200020-2002-2-2002220022-2-20000000000000000000000
χ452222-2-2-1222-2-22-1-1-12-2-222-2-21111-1-1-1-1-1-111-1-111110000-202000-1−i3i311−i3i31-1-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i300000000000000
χ462222-2-2-1222-2-22-1-1-12-2-222-2-21111-1-1-1-1-1-111-1-111110000-202000-1i3−i311i3−i31-1-1−i3i3−i3i3i3−i3i3−i3i3−i3i3−i300000000000000
χ472222-2-2-1222-2-22-1-1-12-2-2-2-22211111111-1-111-1-1-1-1-1-1000020-2000-1−i3i3-1-1−i3i3111i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300000000000000
χ482222-2-2-1222-2-22-1-1-12-2-2-2-22211111111-1-111-1-1-1-1-1-1000020-2000-1i3−i3-1-1i3−i3111−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300000000000000
χ492222-2-2-12-2-2-2-22-1-1-1-22222-2-211-1-1-1-1-1-1-1-111111111000020-20001−i3i3-1-1i3−i3-111i3−i3−i3i3−i3i3−i3i3i3−i3i3−i300000000000000
χ502222-2-2-12-2-2-2-22-1-1-1-22222-2-211-1-1-1-1-1-1-1-111111111000020-20001i3−i3-1-1−i3i3-111−i3i3i3−i3i3−i3i3−i3−i3i3−i3i300000000000000
χ512222-2-2-12-2-2-2-22-1-1-1-222-2-22211-1-11111-1-11111-1-1-1-10000-2020001−i3i311i3−i3-1-1-1i3−i3−i3i3i3−i3i3−i3−i3i3−i3i300000000000000
χ522222-2-2-12-2-2-2-22-1-1-1-222-2-22211-1-11111-1-11111-1-1-1-10000-2020001i3−i311−i3i3-1-1-1−i3i3i3−i3−i3i3−i3i3i3−i3i3−i300000000000000
χ532222-2-2-1-22222-2-1-1-1-22-2000011-1-1−i3−i3i3i311-1-1-1-1i3i3−i3−i32-200020-2001-1-1i3−i3-1-11−i3i31111−i3i3i3−i3−i3i3i3−i300000000000000
χ542222-2-2-1-22222-2-1-1-1-22-2000011-1-1−i3−i3i3i311-1-1-1-1i3i3−i3−i3-22000-20200111i3−i3111−i3i3-1-1-1-1i3−i3−i3i3i3−i3−i3i300000000000000
χ552222-2-2-1-22222-2-1-1-1-22-2000011-1-1i3i3−i3−i311-1-1-1-1−i3−i3i3i32-200020-2001-1-1−i3i3-1-11i3−i31111i3−i3−i3i3i3−i3−i3i300000000000000
χ562222-2-2-1-22222-2-1-1-1-22-2000011-1-1i3i3−i3−i311-1-1-1-1−i3−i3i3i3-22000-20200111−i3i3111i3−i3-1-1-1-1−i3i3i3−i3−i3i3i3−i300000000000000
χ572222-2-2-1-2-2-222-2-1-1-12-2200001111−i3−i3i3i311-1-111i3i3−i3−i32-2000-20200-1-1-1−i3i311-1i3−i311-1-1−i3i3i3−i3i3−i3−i3i300000000000000
χ582222-2-2-1-2-2-222-2-1-1-12-2200001111−i3−i3i3i311-1-111i3i3−i3−i3-2200020-200-111−i3i3-1-1-1i3−i3-1-111i3−i3−i3i3−i3i3i3−i300000000000000
χ592222-2-2-1-2-2-222-2-1-1-12-2200001111i3i3−i3−i311-1-111−i3−i3i3i32-2000-20200-1-1-1i3−i311-1−i3i311-1-1i3−i3−i3i3−i3i3i3−i300000000000000
χ602222-2-2-1-2-2-222-2-1-1-12-2200001111i3i3−i3−i311-1-111−i3−i3i3i3-2200020-200-111i3−i3-1-1-1−i3i3-1-111−i3i3i3−i3i3−i3−i3i300000000000000
χ6122-2-22-22-2002-22-22-20002i−2i2i−2i2-2002i−2i2i−2i2-22-2002i−2i2i−2i00000000000000000000000000000000002i−2i0000002-200
χ6222-2-22-22-2002-22-22-20002i−2i2i−2i2-2002i−2i2i−2i2-22-2002i−2i2i−2i0000000000000000000000000000000000−2i2i000000-2200
χ6322-2-22-22-2002-22-22-2000−2i2i−2i2i2-200−2i2i−2i2i2-22-200−2i2i−2i2i00000000000000000000000000000000002i−2i000000-2200
χ6422-2-22-22-2002-22-22-2000−2i2i−2i2i2-200−2i2i−2i2i2-22-200−2i2i−2i2i0000000000000000000000000000000000−2i2i0000002-200
χ6522-2-2-222-200-222-22-20002i−2i−2i2i-22002i−2i2i−2i2-2-2200−2i2i−2i2i000000000000000000000000000000002i−2i0000002-20000
χ6622-2-2-222-200-222-22-20002i−2i−2i2i-22002i−2i2i−2i2-2-2200−2i2i−2i2i00000000000000000000000000000000−2i2i000000-220000
χ6722-2-2-222-200-222-22-2000−2i2i2i−2i-2200−2i2i−2i2i2-2-22002i−2i2i−2i000000000000000000000000000000002i−2i000000-220000
χ6822-2-2-222-200-222-22-2000−2i2i2i−2i-2200−2i2i−2i2i2-2-22002i−2i2i−2i00000000000000000000000000000000−2i2i0000002-20000
χ6944-4-44-44400-44-4-44-400000004-4000000-44-440000000000000000000000000000000000000000000000000000
χ7044-4-44-4-2400-44-42-220000000-220023−23−23232-22-20023−23−23230000000000000000000000000000000000000000000000
χ7144-4-44-4-2400-44-42-220000000-2200−232323−232-22-200−232323−230000000000000000000000000000000000000000000000
χ7244-4-44-4-2-4004-442-220004i−4i4i−4i-2200−2i2i−2i2i-22-2200−2i2i−2i2i0000000000000000000000000000000000000000000000
χ7344-4-44-4-2-4004-442-22000−4i4i−4i4i-22002i−2i2i−2i-22-22002i−2i2i−2i0000000000000000000000000000000000000000000000
χ7444-4-4-4444004-4-4-44-40000000-44000000-444-40000000000000000000000000000000000000000000000000000
χ7544-4-4-44-24004-4-42-2200000002-20023−23−23232-2-2200−232323−230000000000000000000000000000000000000000000000
χ7644-4-4-44-24004-4-42-2200000002-200−232323−232-2-220023−23−23230000000000000000000000000000000000000000000000
χ7744-4-4-44-2-400-4442-220004i−4i−4i4i2-200−2i2i−2i2i-222-2002i−2i2i−2i0000000000000000000000000000000000000000000000
χ7844-4-4-44-2-400-4442-22000−4i4i4i−4i2-2002i−2i2i−2i-222-200−2i2i−2i2i0000000000000000000000000000000000000000000000
χ794-4-4400404i−4i000-4-4400000000000000000004i−4i00000000000000000000000000000000000000002i−2i2-2000000
χ804-4-4400404i−4i000-4-4400000000000000000004i−4i0000000000000000000000000000000000000000−2i2i-22000000
χ814-4-440040−4i4i000-4-440000000000000000000−4i4i00000000000000000000000000000000000000002i−2i-22000000
χ824-4-440040−4i4i000-4-440000000000000000000−4i4i0000000000000000000000000000000000000000−2i2i2-2000000
χ838-88-80080000008-8-800000000000000000000000000000000000000000000000000000000000000000000000
χ848-88-800-4000000-444000000000−4i34i3000000000000000000000000000000000000000000000000000000000000
χ858-88-800-4000000-4440000000004i3−4i3000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-408i−8i00044-40000000000000000000−4i4i00000000000000000000000000000000000000000000000000
χ878-8-8800-40−8i8i00044-400000000000000000004i−4i00000000000000000000000000000000000000000000000000

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