Finite Group Databasebeta

← Group #10858775

Character table — Group #10858775

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order12222222344446666666444444888812121212121212122222224446666881212121212122424242424242424444488884121212124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111111-1-11111111-1-1-1-111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-111-1-1-1-111-111-1-1-1
χ6111111111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-111-1-111-1-11-1-1111
χ7111111111111111111111111-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-11-1-111-1-111-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-111111-1-11111-1-1111-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1111-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-111-1
χ1311111111111111111111-1-1-1-1-1-11111111-1-1-1-11111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11-1-111-1-11111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-111-1-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-111-111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-111-1-1-1-1111-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-2-22222-2222200-200000000-2-200000000000022-2-20000000000000-200000
χ18222222222-2-2-2-222222220000220000-2-2-22222-2-2-2-2-200-200000000-2-2000000000000-2-2220000000000000200000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222220020000000022000000000000-2-2-2-20000000000000200000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-2002000000002200000000000022220000000000000-200000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-1-11111-10000-2-2-2221111-2-211-1-1-1-1-1-1-1-1111100000000-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-11111-10000-2-2-2-2-211112211-1-1-1-11111-1-1-1-100000000211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-10000-2-22-2-2111122-1-11111-1-1-1-1-1-1-1-100000000-211110000000000
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
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-11111-1000022-2-2-2-1-1-1-1-2-2111111-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-1-11111-1000022-222-1-1-1-1221111111111-1-1-1-100000000-2-1-1110000000000
χ2922-222-2-2-2222-2-222-22-2-2-2000000000022-20000-222-2-22-200022-2-20000000000000000002-20000000002-200000000
χ3022-222-2-2-2222-2-222-22-2-2-2000000000022-20000-222-2-2-22000-2-2220000000000000000002-2000000000-2200000000
χ3122-222-2-2-2222-2-222-22-2-2-2000000000022-20000-2-2-2222-200022-2-2000000000000000000-22000000000-2200000000
χ3222-222-2-2-2222-2-222-22-2-2-2000000000022-20000-2-2-222-22000-2-222000000000000000000-220000000002-200000000
χ3322-222-2-2-22-2-22222-22-2-2-22i2i−2i−2i000000-2-220000222-2-200000000000002i2i−2i−2i0000000000-22000000000002i−2i000000
χ3422-222-2-2-22-2-22222-22-2-2-22i2i−2i−2i000000-2-2200002-2-22200000000000002i2i−2i−2i00000000002-200000000000−2i2i000000
χ3522-222-2-2-22-2-22222-22-2-2-2−2i−2i2i2i000000-2-220000222-2-20000000000000−2i−2i2i2i0000000000-2200000000000−2i2i000000
χ3622-222-2-2-22-2-22222-22-2-2-2−2i−2i2i2i000000-2-2200002-2-2220000000000000−2i−2i2i2i00000000002-2000000000002i−2i000000
χ372-222-2-2-2222-22-2-2-222-2-222i−2i2i−2i0000002-220000-2000000000000000002i−2i2i−2i0000000000002i2i−2i−2i00000000002-2000
χ382-222-2-2-2222-22-2-2-222-2-222i−2i2i−2i0000002-220000-2000000000000000002i−2i2i−2i000000000000−2i−2i2i2i0000000000-22000
χ392-222-2-2-2222-22-2-2-222-2-22−2i2i−2i2i0000002-220000-200000000000000000−2i2i−2i2i0000000000002i2i−2i−2i0000000000-22000
χ402-222-2-2-2222-22-2-2-222-2-22−2i2i−2i2i0000002-220000-200000000000000000−2i2i−2i2i000000000000−2i−2i2i2i00000000002-2000
χ412-22-22-22-2200002-22-2-22-200002-2−i2−i2i2i200022-2-202-22-2000000000−i2i2000000−i2−i2i2i2−i2−i2i2i22-200−i2i2−i2i2000000000000−i2i20
χ422-22-22-22-2200002-22-2-22-200002-2−i2−i2i2i200022-2-20-22-22000000000−i2i2000000−i2−i2i2i2−i2−i2i2i2-2200i2−i2i2−i2000000000000i2−i20
χ432-22-22-22-2200002-22-2-22-200002-2i2i2−i2−i200022-2-202-22-2000000000i2−i2000000i2i2−i2−i2i2i2−i2−i22-200i2−i2i2−i2000000000000i2−i20
χ442-22-22-22-2200002-22-2-22-200002-2i2i2−i2−i200022-2-20-22-22000000000i2−i2000000i2i2−i2−i2i2i2−i2−i2-2200−i2i2−i2i2000000000000−i2i20
χ452-22-22-22-2200002-22-2-22-20000-22−i2−i2i2i2000-2-22202-22-2000000000i2−i2000000−i2−i2i2i2i2i2−i2−i2-2200−i2i2−i2i2000000000000i2−i20
χ462-22-22-22-2200002-22-2-22-20000-22−i2−i2i2i2000-2-2220-22-22000000000i2−i2000000−i2−i2i2i2i2i2−i2−i22-200i2−i2i2−i2000000000000−i2i20
χ472-22-22-22-2200002-22-2-22-20000-22i2i2−i2−i2000-2-22202-22-2000000000−i2i2000000i2i2−i2−i2−i2−i2i2i2-2200i2−i2i2−i2000000000000−i2i20
χ482-22-22-22-2200002-22-2-22-20000-22i2i2−i2−i2000-2-2220-22-22000000000−i2i2000000i2i2−i2−i2−i2−i2i2i22-200−i2i2−i2i2000000000000i2−i20
χ492-2-22-222-22-222-2-2-2-2222-22-2-22002i−2i2i−2i-2220000-200000002i−2i000000002-2-222i−2i2i−2i00000000000002i−2i000000000000
χ502-2-22-222-22-222-2-2-2-2222-22-2-2200−2i2i−2i2i-2220000-20000000−2i2i000000002-2-22−2i2i−2i2i0000000000000−2i2i000000000000
χ512-2-22-222-22-222-2-2-2-2222-2-222-2002i−2i2i−2i-2220000-20000000−2i2i00000000-222-22i−2i2i−2i0000000000000−2i2i000000000000
χ522-2-22-222-22-222-2-2-2-2222-2-222-200−2i2i−2i2i-2220000-200000002i−2i00000000-222-2−2i2i−2i2i00000000000002i−2i000000000000
χ532-2-22-222-2-1-222-2111-1-1-112-2-22002i−2i2i−2i1-1-1−i3i3−i3i3100000002i−2i−i3i3−i3i300−i3i3-111-1−ii−ii3−33−3000000000−ii3−30000000000
χ542-2-22-222-2-1-222-2111-1-1-112-2-22002i−2i2i−2i1-1-1i3−i3i3−i3100000002i−2ii3−i3i3−i300i3−i3-111-1−ii−ii−33−33000000000−ii−330000000000
χ552-2-22-222-2-1-222-2111-1-1-112-2-2200−2i2i−2i2i1-1-1−i3i3−i3i310000000−2i2i−i3i3−i3i300−i3i3-111-1i−ii−i−33−33000000000i−i−330000000000
χ562-2-22-222-2-1-222-2111-1-1-112-2-2200−2i2i−2i2i1-1-1i3−i3i3−i310000000−2i2ii3−i3i3−i300i3−i3-111-1i−ii−i3−33−3000000000i−i3−30000000000
χ572-2-22-222-2-1-222-2111-1-1-11-222-2002i−2i2i−2i1-1-1−i3i3−i3i310000000−2i2ii3−i3i3−i300−i3i31-1-11−ii−ii3−33−3000000000i−i−330000000000
χ582-2-22-222-2-1-222-2111-1-1-11-222-2002i−2i2i−2i1-1-1i3−i3i3−i310000000−2i2i−i3i3−i3i300i3−i31-1-11−ii−ii−33−33000000000i−i3−30000000000
χ592-2-22-222-2-1-222-2111-1-1-11-222-200−2i2i−2i2i1-1-1−i3i3−i3i3100000002i−2ii3−i3i3−i300−i3i31-1-11i−ii−i−33−33000000000−ii3−30000000000
χ602-2-22-222-2-1-222-2111-1-1-11-222-200−2i2i−2i2i1-1-1i3−i3i3−i3100000002i−2i−i3i3−i3i300i3−i31-1-11i−ii−i3−33−3000000000−ii−330000000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-20000440000222-2-2-2-22000000-4000000002200000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4000022222222000000400000000-2-200000000000000000000000000000000000
χ63444-4-44-4-440000-444-44-4-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ64444-4-44-4-440000-444-44-4-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ6544-444-4-4-4-244-4-4-2-22-22220000000000-2-220000200004-4000-2-222000000000000000000000000000000000000000
χ6644-444-4-4-4-244-4-4-2-22-22220000000000-2-22000020000-4400022-2-2000000000000000000000000000000000000000
χ6744-444-4-4-4-2-4-444-2-22-22224i4i−4i−4i00000022-20000-200000000000000000−2i−2i2i2i0000000000000000000000000000000
χ6844-444-4-4-4-2-4-444-2-22-2222−4i−4i4i4i00000022-20000-2000000000000000002i2i−2i−2i0000000000000000000000000000000
χ6944-4-4-4-44440000-44-4-4-44400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ7044-4-4-4-44440000-44-4-4-444000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ7144-4-4-4-444-200002-2222-2-200000022−22−2222000−2i32i32i3−2i30000000000000000000000−222−2−i6i6i6−i600000000000000000000000
χ7244-4-4-4-444-200002-2222-2-200000022−22−22220002i3−2i3−2i32i30000000000000000000000−222−2i6−i6−i6i600000000000000000000000
χ7344-4-4-4-444-200002-2222-2-2000000−222222−22000−2i32i32i3−2i300000000000000000000002−2−22i6−i6−i6i600000000000000000000000
χ7444-4-4-4-444-200002-2222-2-2000000−222222−220002i3−2i3−2i32i300000000000000000000002−2−22−i6i6i6−i600000000000000000000000
χ754-444-4-4-444-44-44-4-444-4-440000000000-44-4000040000000000000000000000000000000000000000000000000000
χ764-444-4-4-44-24-44-422-2-222-24i−4i4i−4i000000-22-20000200000000000000000−2i2i−2i2i0000000000000000000000000000000
χ774-444-4-4-44-24-44-422-2-222-2−4i4i−4i4i000000-22-200002000000000000000002i−2i2i−2i0000000000000000000000000000000
χ784-444-4-4-44-2-44-4422-2-222-200000000002-220000-2000000000−2i32i32i3−2i3000000000000000000000000000000000000000
χ794-444-4-4-44-2-44-4422-2-222-200000000002-220000-20000000002i3−2i3−2i32i3000000000000000000000000000000000000000
χ804-44-44-44-4-20000-22-222-2200004-4−2i2−2i22i22i2000-2-22200000000000000−2i22i2000000i2i2−i2−i2i2i2−i2−i200000000000000000000000
χ814-44-44-44-4-20000-22-222-2200004-42i22i2−2i2−2i2000-2-222000000000000002i2−2i2000000−i2−i2i2i2−i2−i2i2i200000000000000000000000
χ824-44-44-44-4-20000-22-222-220000-44−2i2−2i22i22i200022-2-2000000000000002i2−2i2000000i2i2−i2−i2−i2−i2i2i200000000000000000000000
χ834-44-44-44-4-20000-22-222-220000-442i22i2−2i2−2i200022-2-200000000000000−2i22i2000000−i2−i2i2i2i2i2−i2−i200000000000000000000000
χ844-4-44-444-444-4-44-4-4-4444-400000000004-4-4000040000000000000000000000000000000000000000000000000000
χ854-4-44-444-4-24-4-44222-2-2-220000000000-222−2i32i3−2i32i3-20000000000000002i3−2i300000000000000000000000000000000000
χ864-4-44-444-4-24-4-44222-2-2-220000000000-2222i3−2i32i3−2i3-2000000000000000−2i32i300000000000000000000000000000000000
χ874-4-4-444-44400004-4-4-44-440000000000000000004-4-44000000000000000000000000000000000000000000000000
χ884-4-4-444-44400004-4-4-44-44000000000000000000-444-4000000000000000000000000000000000000000000000000
χ89888-8-88-8-8-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-888-88-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000000000

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