Finite Group Databasebeta

← Group #10828737

Character table — Group #10828737

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888888888888888882424242424242424242424244848
order1222223444444666121212122244444666666121212121212444444888812121212121212121212121212121212242424242424242424444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-11-1-1111111111111-111-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-111
χ61111111111111111111111-1-11-1-1111111111111-111-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1
χ71111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-11111-1-1
χ81111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-111-1-1-1-111
χ911111111-1-1111111-1-1-1-1-1-111-11111-1-1-1-1111-1-11-111-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1-1-11111-1-11-1
χ1011111111-1-1111111-1-1-1-1-1-111-11111-1-1-1-1111-1-11-111-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1111-1-1-1-111-11
χ1111111111-1-1111111-1-1-1-1-1-111-11111-1-1-1-1111-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-1-111-1-111-11
χ1211111111-1-1111111-1-1-1-1-1-111-11111-1-1-1-1111-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1111-1-111-1-11-1
χ1311111111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1111-1-1-1-1-1111-1
χ1411111111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1-1-111111-1-1-11
χ1511111111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-111-1-111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1111-1-1-111-1-1-11
χ1611111111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-111-1-111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1-1-1111-1-1111-1
χ172222222-222-2-2-22222222-2-20020022-2-2-2-2-2-2-222-200000000000000000000000000000000000002-202-2000000
χ182222222-222-2-2-22222222-2-20020022-2-2-2-2-2-2-222-20000000000000000000000000000000000000-220-22000000
χ192222222-2-2-2-2-2-2222-2-2-2-22200-200222222-2-2-2-2-2-200000000000000000000000000000000000002-20-22000000
χ202222222-2-2-2-2-2-2222-2-2-2-22200-200222222-2-2-2-2-2-20000000000000000000000000000000000000-2202-2000000
χ21222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-12-2-22-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000
χ23222222-1222222-1-1-1-1-1-1-122-2-22-2-2-1-1-1-1-1-1-1-1-1-1-1-1-222-222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000
χ24222222-1222222-1-1-1-1-1-1-122-2-22-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000
χ25222222-12-2-2222-1-1-11111-2-222-222-1-11111-1-1-111-1-222-2-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000000000
χ26222222-12-2-2222-1-1-11111-2-222-222-1-11111-1-1-111-1-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000
χ27222222-12-2-2222-1-1-11111-2-2-2-2-2-2-2-1-11111-1-1-111-12222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000
χ28222222-12-2-2222-1-1-11111-2-2-2-2-2-2-2-1-11111-1-1-111-12-2-222222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000
χ292222-2-222222-2-222222222-222-2-2-2-2-222-2-22-2-2-2-22-200200000022-2-222-2-2000000000000000000000000000000
χ302222-2-222222-2-222222222-2-2-2-222-2-222-2-22-2-2-2-22200-2000000-2-222-2-222000000000000000000000000000000
χ312222-2-222-2-22-2-2222-2-2-2-2-22222-2-2-2-2-2-2222-2-2222200-200000022-2-2-2-222000000000000000000000000000000
χ322222-2-222-2-22-2-2222-2-2-2-2-22-2-2222-2-2-2-2222-2-2222-2002000000-2-22222-2-2000000000000000000000000000000
χ332222-2-22-222-2222222222-2200-200-2-2-2-222-222-2-2-2000000000000000000000000000000000022-200-200000000
χ342222-2-22-222-2222222222-2200-200-2-2-2-222-222-2-2-20000000000000000000000000000000000-2-2200200000000
χ352222-2-22-2-2-2-222222-2-2-2-22-200200-2-222-2-2-22222-200000000000000000000000000000000002-2-200200000000
χ362222-2-22-2-2-2-222222-2-2-2-22-200200-2-222-2-2-22222-20000000000000000000000000000000000-22200-200000000
χ372222-2-2-12222-2-2-1-1-1-1-1-1-12-222-2-2-211-1-111-11111-1-2002000000-1-111-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000
χ382222-2-2-12222-2-2-1-1-1-1-1-1-12-222-2-2-211-1-111-11111-1-2002000000-1-111-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000
χ392222-2-2-12222-2-2-1-1-1-1-1-1-12-2-2-2-22211-1-111-11111-1200-200000011-1-111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000
χ402222-2-2-12222-2-2-1-1-1-1-1-1-12-2-2-2-22211-1-111-11111-1200-200000011-1-111-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000
χ412222-2-2-12-2-22-2-2-1-1-11111-22222-2-21111-1-1-111-1-1-1200-2000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000
χ422222-2-2-12-2-22-2-2-1-1-11111-22222-2-21111-1-1-111-1-1-1200-2000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000
χ432222-2-2-12-2-22-2-2-1-1-11111-22-2-22221111-1-1-111-1-1-1-200200000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000
χ442222-2-2-12-2-22-2-2-1-1-11111-22-2-22221111-1-1-111-1-1-1-200200000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000
χ452-22-22-22-20022-22-2-20000002i−2i02i−2i2-20000-22-200200002i−2i002-22i−2i2i−2i000000002i−2i2i−2i00002-22-200000000000000
χ462-22-22-22-20022-22-2-20000002i−2i02i−2i2-20000-22-20020000−2i2i00-222i−2i2i−2i00000000−2i2i−2i2i0000-22-2200000000000000
χ472-22-22-22-20022-22-2-2000000−2i2i0−2i2i2-20000-22-200200002i−2i00-22−2i2i−2i2i000000002i−2i2i−2i0000-22-2200000000000000
χ482-22-22-22-20022-22-2-2000000−2i2i0−2i2i2-20000-22-20020000−2i2i002-2−2i2i−2i2i00000000−2i2i−2i2i00002-22-200000000000000
χ492-22-22-2-1-20022-2-111−i3−i3i3i3002i−2i02i−2i-11−i3i3−i3i31-11−i3i3-100002i−2i002-2−ii−ii3−33−33−33−3−ii−ii−i3i3−i3i3-11-1100000000000000
χ502-22-22-2-1-20022-2-111−i3−i3i3i3002i−2i02i−2i-11−i3i3−i3i31-11−i3i3-10000−2i2i00-22−ii−ii3−33−3−33−33i−ii−ii3−i3i3−i31-11-100000000000000
χ512-22-22-2-1-20022-2-111−i3−i3i3i300−2i2i0−2i2i-11−i3i3−i3i31-11−i3i3-100002i−2i00-22i−ii−i−33−333−33−3−ii−iii3−i3i3−i31-11-100000000000000
χ522-22-22-2-1-20022-2-111−i3−i3i3i300−2i2i0−2i2i-11−i3i3−i3i31-11−i3i3-10000−2i2i002-2i−ii−i−33−33−33−33i−ii−i−i3i3−i3i3-11-1100000000000000
χ532-22-22-2-1-20022-2-111i3i3−i3−i3002i−2i02i−2i-11i3−i3i3−i31-11i3−i3-100002i−2i002-2−ii−ii−33−33−33−33−ii−iii3−i3i3−i3-11-1100000000000000
χ542-22-22-2-1-20022-2-111i3i3−i3−i3002i−2i02i−2i-11i3−i3i3−i31-11i3−i3-10000−2i2i00-22−ii−ii−33−333−33−3i−ii−i−i3i3−i3i31-11-100000000000000
χ552-22-22-2-1-20022-2-111i3i3−i3−i300−2i2i0−2i2i-11i3−i3i3−i31-11i3−i3-100002i−2i00-22i−ii−i3−33−3−33−33−ii−ii−i3i3−i3i31-11-100000000000000
χ562-22-22-2-1-20022-2-111i3i3−i3−i300−2i2i0−2i2i-11i3−i3i3−i31-11i3−i3-10000−2i2i002-2i−ii−i3−33−33−33−3i−ii−ii3−i3i3−i3-11-1100000000000000
χ572-22-2-222-2002-222-2-20000002i−2i0−2i2i-220000-2-2200202i−2i0002-2002i−2i−2i2i00002i−2i−2i2i00002-2-22000000000000000000
χ582-22-2-222-2002-222-2-20000002i−2i0−2i2i-220000-2-220020−2i2i000-22002i−2i−2i2i0000−2i2i2i−2i0000-222-2000000000000000000
χ592-22-2-222-2002-222-2-2000000−2i2i02i−2i-220000-2-2200202i−2i000-2200−2i2i2i−2i00002i−2i−2i2i0000-222-2000000000000000000
χ602-22-2-222-2002-222-2-2000000−2i2i02i−2i-220000-2-220020−2i2i0002-200−2i2i2i−2i0000−2i2i2i−2i00002-2-22000000000000000000
χ612-22-2-22-1-2002-22-111−i3−i3i3i3002i−2i0−2i2i1-1−i3i3i3−i311-1i3−i3-102i−2i0002-200−iii−i3−3−33−iii−i3−3−33-111-1−i3i3i3−i300000000000000
χ622-22-2-22-1-2002-22-111−i3−i3i3i3002i−2i0−2i2i1-1−i3i3i3−i311-1i3−i3-10−2i2i000-2200−iii−i3−3−33i−i−ii−333−31-1-11i3−i3−i3i300000000000000
χ632-22-2-22-1-2002-22-111−i3−i3i3i300−2i2i02i−2i1-1−i3i3i3−i311-1i3−i3-102i−2i000-2200i−i−ii−333−3−iii−i3−3−331-1-11i3−i3−i3i300000000000000
χ642-22-2-22-1-2002-22-111−i3−i3i3i300−2i2i02i−2i1-1−i3i3i3−i311-1i3−i3-10−2i2i0002-200i−i−ii−333−3i−i−ii−333−3-111-1−i3i3i3−i300000000000000
χ652-22-2-22-1-2002-22-111i3i3−i3−i3002i−2i0−2i2i1-1i3−i3−i3i311-1−i3i3-102i−2i0002-200−iii−i−333−3−iii−i−333−3-111-1i3−i3−i3i300000000000000
χ662-22-2-22-1-2002-22-111i3i3−i3−i3002i−2i0−2i2i1-1i3−i3−i3i311-1−i3i3-10−2i2i000-2200−iii−i−333−3i−i−ii3−3−331-1-11−i3i3i3−i300000000000000
χ672-22-2-22-1-2002-22-111i3i3−i3−i300−2i2i02i−2i1-1i3−i3−i3i311-1−i3i3-102i−2i000-2200i−i−ii3−3−33−iii−i−333−31-1-11−i3i3i3−i300000000000000
χ682-22-2-22-1-2002-22-111i3i3−i3−i300−2i2i02i−2i1-1i3−i3−i3i311-1−i3i3-10−2i2i0002-200i−i−ii3−3−33i−i−ii3−3−33-111-1i3−i3−i3i300000000000000
χ69444444-2-444-4-4-4-2-2-2-2-2-2-2-4-400400-2-22222222-2-22000000000000000000000000000000000000000000000000
χ70444444-2-4-4-4-4-4-4-2-2-222224400-400-2-2-2-2-2-2222222000000000000000000000000000000000000000000000000
χ714444-4-4-2-444-444-2-2-2-2-2-2-2-4400-4002222-2-22-2-2222000000000000000000000000000000000000000000000000
χ724444-4-4-2-4-4-4-444-2-2-222224-40040022-2-2222-2-2-2-22000000000000000000000000000000000000000000000000
χ734-44-44-44400-4-444-4-4000000000004-400004-4400-4000000000000000000000000000000000000000000000000
χ744-44-44-4-2400-4-44-222−2i3−2i32i32i30000000-222i3−2i32i3−2i3-22-2−2i32i32000000000000000000000000000000000000000000000000
χ754-44-44-4-2400-4-44-2222i32i3−2i3−2i30000000-22−2i32i3−2i32i3-22-22i3−2i32000000000000000000000000000000000000000000000000
χ764-44-4-444400-44-44-4-400000000000-44000044-400-4000000000000000000000000000000000000000000000000
χ774-44-4-44-2400-44-4-222−2i3−2i32i32i300000002-22i3−2i3−2i32i3-2-222i3−2i32000000000000000000000000000000000000000000000000
χ784-44-4-44-2400-44-4-2222i32i3−2i3−2i300000002-2−2i32i32i3−2i3-2-22−2i32i32000000000000000000000000000000000000000000000000
χ794-4-4400404i−4i000-44-44i−4i4i−4i00000000000000000000000000000000000000000000000000000000000002i−2i2-200
χ804-4-4400404i−4i000-44-44i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000−2i2i-2200
χ814-4-440040−4i4i000-44-4−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000002i−2i-2200
χ824-4-440040−4i4i000-44-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000−2i2i2-200
χ8388-8-8008000000-8-8800000000000000000000000000000000000000000000000000000000000000000000000
χ8488-8-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000000
χ8588-8-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-408i−8i0004-44−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000
χ878-8-8800-40−8i8i0004-444i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000

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