Finite Group Databasebeta

← Group #10855228

Character table — Group #10855228

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order12222222344446666666222244888812121212121212124444444446666881212121212122424242424242424444488884121212122244444882
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
χ5111111111111111111111111-1-1111111-1-1-1-1111111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-11111-1-1-111-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1111-1-1111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-1-1-1-111111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111111111-1-111111-1-1-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111111-1-1-1-1-111-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111-1-1111-1-11111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-111-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-111-1-1-1-111-1-11111-1-1-1-11111-1-1111111-1-1-111-1-11-1-111-1-11
χ17222222222-2-2-2-222222220000220000-2-22222-2-2222200-200000000-2-2000000000000-2-22200000000000-20000000
χ18222222222-2-2-2-222222220000220000-2-22222-2-2-2-2-2-200-200000000-2-200000000000022-2-20000000000020000000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222220020000000022000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-20020000000022000000000000222200000000000-20000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-11111-1-10000-2-2-222-1-1-1-1-2-2111111-1-1-1-1111100000000-211-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-11111-1-10000-2-2-2-2-2-1-1-1-1221111111111-1-1-1-1000000002-1-1110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-10000-2-22-2-2111122-1-11111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-10000-2-22221111-2-2-1-1111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-1000022-2-2-21111-2-211-1-1-1-1-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-1000022-22211112211-1-1-1-11111-1-1-1-100000000-211-1-10000000000
χ292222-2-2-2-22-22-222-2-222-2-222-2-2002i2i−2i−2i2-200002-200000002i−2i22-2-2000000002i2i−2i−2i0000000000000002i−2i0000000000
χ302222-2-2-2-22-22-222-2-222-2-222-2-200−2i−2i2i2i2-200002-20000000−2i2i22-2-200000000−2i−2i2i2i000000000000000−2i2i0000000000
χ312222-2-2-2-22-22-222-2-222-2-2-2-222002i2i−2i−2i2-200002-20000000−2i2i-2-222000000002i2i−2i−2i000000000000000−2i2i0000000000
χ322222-2-2-2-22-22-222-2-222-2-2-2-22200−2i−2i2i2i2-200002-200000002i−2i-2-22200000000−2i−2i2i2i0000000000000002i−2i0000000000
χ332222-2-2-2-2-1-22-22-111-1-11122-2-2002i2i−2i−2i-1133−3−3-1100000002i−2i-1-111003−333−3−3−i−iii−i3−i3i3i3000000000−i3i3−ii0000000000
χ342222-2-2-2-2-1-22-22-111-1-11122-2-2002i2i−2i−2i-11−3−333-1100000002i−2i-1-11100−33−3−333−i−iiii3i3−i3−i3000000000i3−i3−ii0000000000
χ352222-2-2-2-2-1-22-22-111-1-11122-2-200−2i−2i2i2i-1133−3−3-110000000−2i2i-1-111003−333−3−3ii−i−ii3i3−i3−i3000000000i3−i3i−i0000000000
χ362222-2-2-2-2-1-22-22-111-1-11122-2-200−2i−2i2i2i-11−3−333-110000000−2i2i-1-11100−33−3−333ii−i−i−i3−i3i3i3000000000−i3i3i−i0000000000
χ372222-2-2-2-2-1-22-22-111-1-111-2-222002i2i−2i−2i-1133−3−3-110000000−2i2i11-1-1003−3−3−333−i−iii−i3−i3i3i3000000000i3−i3i−i0000000000
χ382222-2-2-2-2-1-22-22-111-1-111-2-222002i2i−2i−2i-11−3−333-110000000−2i2i11-1-100−3333−3−3−i−iiii3i3−i3−i3000000000−i3i3i−i0000000000
χ392222-2-2-2-2-1-22-22-111-1-111-2-22200−2i−2i2i2i-1133−3−3-1100000002i−2i11-1-1003−3−3−333ii−i−ii3i3−i3−i3000000000−i3i3−ii0000000000
χ402222-2-2-2-2-1-22-22-111-1-111-2-22200−2i−2i2i2i-11−3−333-1100000002i−2i11-1-100−3333−3−3ii−i−i−i3−i3i3i3000000000i3−i3−ii0000000000
χ4122-2-222-2-22000022-2-2-22-200002-2−i2i2−i2i2002-22-2002i2i−2i−2i000000000−i2i2000000−i2i2−i2i2−i2i2−i2i2002i−2i22−2−20000000000002−20
χ4222-2-222-2-22000022-2-2-22-200002-2−i2i2−i2i2002-22-200−2i−2i2i2i000000000−i2i2000000−i2i2−i2i2−i2i2−i2i200−2i2i−2−222000000000000−220
χ4322-2-222-2-22000022-2-2-22-200002-2i2−i2i2−i2002-22-2002i2i−2i−2i000000000i2−i2000000i2−i2i2−i2i2−i2i2−i2002i−2i−2−222000000000000−220
χ4422-2-222-2-22000022-2-2-22-200002-2i2−i2i2−i2002-22-200−2i−2i2i2i000000000i2−i2000000i2−i2i2−i2i2−i2i2−i200−2i2i22−2−20000000000002−20
χ4522-2-222-2-22000022-2-2-22-20000-22−i2i2−i2i200-22-22002i2i−2i−2i000000000i2−i2000000−i2i2−i2i2i2−i2i2−i200−2i2i22−2−2000000000000−220
χ4622-2-222-2-22000022-2-2-22-20000-22−i2i2−i2i200-22-2200−2i−2i2i2i000000000i2−i2000000−i2i2−i2i2i2−i2i2−i2002i−2i−2−2220000000000002−20
χ4722-2-222-2-22000022-2-2-22-20000-22i2−i2i2−i200-22-22002i2i−2i−2i000000000−i2i2000000i2−i2i2−i2−i2i2−i2i200−2i2i−2−2220000000000002−20
χ4822-2-222-2-22000022-2-2-22-20000-22i2−i2i2−i200-22-2200−2i−2i2i2i000000000−i2i2000000i2−i2i2−i2−i2i2−i2i2002i−2i22−2−2000000000000−220
χ492-22-22-22-222-2-22-2222-2-2-22-22-2000000220000-2-22i−2i2i−2i000002-22-200000000000000002i−2i00000000000000002i−2i000
χ502-22-22-22-222-2-22-2222-2-2-22-22-2000000220000-2-2−2i2i−2i2i000002-22-20000000000000000−2i2i0000000000000000−2i2i000
χ512-22-22-22-222-2-22-2222-2-2-2-22-22000000220000-2-22i−2i2i−2i00000-22-2200000000000000002i−2i0000000000000000−2i2i000
χ522-22-22-22-222-2-22-2222-2-2-2-22-22000000220000-2-2−2i2i−2i2i00000-22-220000000000000000−2i2i00000000000000002i−2i000
χ532-22-22-22-22-222-2-2222-2-2-20000000000-2-20000222i−2i2i−2i2i−2i000000000002i−2i2i−2i00000000−2i2i000000000000002-200000
χ542-22-22-22-22-222-2-2222-2-2-20000000000-2-20000222i−2i2i−2i−2i2i00000000000−2i2i−2i2i00000000−2i2i00000000000000-2200000
χ552-22-22-22-22-222-2-2222-2-2-20000000000-2-2000022−2i2i−2i2i2i−2i000000000002i−2i2i−2i000000002i−2i00000000000000-2200000
χ562-22-22-22-22-222-2-2222-2-2-20000000000-2-2000022−2i2i−2i2i−2i2i00000000000−2i2i−2i2i000000002i−2i000000000000002-200000
χ572-22-2-22-222-2-222-2-2-22-2222-2-220000002-20000-220000000002-2-22000000000000000000002-22-2000002-200000000
χ582-22-2-22-222-2-222-2-2-22-2222-2-220000002-20000-220000000002-2-2200000000000000000000-22-2200000-2200000000
χ592-22-2-22-222-2-222-2-2-22-222-222-20000002-20000-22000000000-222-2000000000000000000002-22-200000-2200000000
χ602-22-2-22-222-2-222-2-2-22-222-222-20000002-20000-22000000000-222-200000000000000000000-22-22000002-200000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2000044000022-2-2-2-222000000-4000000002200000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4000022222222000000400000000-2-200000000000000000000000000000000000
χ634444-4-4-4-444-44-44-4-444-4-40000000000-440000-440000000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-24-44-4-222-2-22200000000002-22323−23−232-2000000000000000−232300000000000000000000000000000000000
χ654444-4-4-4-4-24-44-4-222-2-22200000000002-2−23−2323232-200000000000000023−2300000000000000000000000000000000000
χ6644-4-444-4-4-20000-2-2222-2200004-4−2i22i2−2i22i200-22-22000000000000000−2i22i2000000i2−i2i2−i2i2−i2i2−i200000000000000000000000
χ6744-4-444-4-4-20000-2-2222-2200004-42i2−2i22i2−2i200-22-220000000000000002i2−2i2000000−i2i2−i2i2−i2i2−i2i200000000000000000000000
χ6844-4-444-4-4-20000-2-2222-220000-44−2i22i2−2i22i2002-22-20000000000000002i2−2i2000000i2−i2i2−i2−i2i2−i2i200000000000000000000000
χ6944-4-444-4-4-20000-2-2222-220000-442i2−2i22i2−2i2002-22-2000000000000000−2i22i2000000−i2i2−i2i2i2−i2i2−i200000000000000000000000
χ7044-4-4-4-444400004-44-4-4-4400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ7144-4-4-4-444400004-44-4-4-44000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ7244-4-4-4-444-20000-22-2222-200000022−22−22220023−23−232300000000000000000000000−222−2−666−600000000000000000000000
χ7344-4-4-4-444-20000-22-2222-200000022−22−222200−232323−2300000000000000000000000−222−26−6−6600000000000000000000000
χ7444-4-4-4-444-20000-22-2222-2000000−222222−220023−23−2323000000000000000000000002−2−226−6−6600000000000000000000000
χ7544-4-4-4-444-20000-22-2222-2000000−222222−2200−232323−23000000000000000000000002−2−22−666−600000000000000000000000
χ764-44-44-44-4-24-4-442-2-2-22224-44-4000000-2-2000022000000000-22-22000000000000000000000000000000000000000
χ774-44-44-44-4-24-4-442-2-2-2222-44-44000000-2-20000220000000002-22-2000000000000000000000000000000000000000
χ784-44-44-44-4-2-444-42-2-2-22220000000000220000-2-200004i−4i00000000000−2i2i−2i2i0000000000000000000000000000000
χ794-44-44-44-4-2-444-42-2-2-22220000000000220000-2-20000−4i4i000000000002i−2i2i−2i0000000000000000000000000000000
χ804-44-4-44-44444-4-4-4-4-44-4440000000000-4400004-40000000000000000000000000000000000000000000000000000
χ814-44-4-44-44-244-4-4222-22-2-200000000002-20000-2200000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ824-44-4-44-44-244-4-4222-22-2-200000000002-20000-22000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ834-44-4-44-44-2-4-444222-22-2-24-4-44000000-2200002-2000000000-222-2000000000000000000000000000000000000000
χ844-44-4-44-44-2-4-444222-22-2-2-444-4000000-2200002-20000000002-2-22000000000000000000000000000000000000000
χ854-4-444-4-4440000-44-4-44-440000000000000000004-4-44000000000000000000000000000000000000000000000000
χ864-4-444-4-4440000-44-4-44-44000000000000000000-444-4000000000000000000000000000000000000000000000000
χ874-4-44-444-440000-4-44-444-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ884-4-44-444-440000-4-44-444-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ898-8-888-8-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88-888-8-4000044-44-4-440000000000000000000000000000000000000000000000000000000000000000000000

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