Finite Group Databasebeta

← Group #10699171

Character table — Group #10699171

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order122222344444466644466121212121212121288881212242424242424242424668812122424242444448888888822
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111
χ9222222222-222-2222-2-2-222-2-2-2222-220000-2-200000000000000000000000022-2-2000000
χ10222222222-222-2222-2-2-222-2-2-2222-220000-2-2000000000000000000000000-2-222000000
χ112222222-2-22-2-222222-2-222222-2-2-22-20000-2-2000000000000000000000000000000002-2
χ122222222-2-22-2-222222-2-222222-2-2-22-20000-2-200000000000000000000000000000000-22
χ132222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-20000220000000000002i−2i002i2i−2i−2i00000000000000
χ142222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-2000022000000000000−2i2i00−2i−2i2i2i00000000000000
χ15222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100000000000000
χ16222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-211111100000000000000
χ17222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-2-2-1-1111100000000000000
χ18222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2112211-1-1-1-100000000000000
χ19222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111110000-1-13333−3−3−3−300−i3i32i−2i−i3i3−i−iii00000000000000
χ20222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111110000-1-13333−3−3−3−300i3−i3−2i2ii3−i3ii−i−i00000000000000
χ21222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111110000-1-1−3−3−3−3333300−i3i3−2i2i−i3i3ii−i−i00000000000000
χ22222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111110000-1-1−3−3−3−3333300i3−i32i−2ii3−i3−i−iii00000000000000
χ232222-2-22222-2-22222-22-2-2-22-2-22-2-22200002-2000000002-22200-2-2000000000000000000
χ242222-2-22222-2-22222-22-2-2-22-2-22-2-22200002-200000000-22-2-20022000000000000000000
χ252222-2-2222-2-2-2-22222-22-2-2-2222-2-2-220000-22000000000000000000002i2i−2i−2i0000000000
χ262222-2-2222-2-2-2-22222-22-2-2-2222-2-2-220000-2200000000000000000000−2i−2i2i2i0000000000
χ272222-2-22-2-22222222-2-22-2-22-2-2-2222-20000-22000000000000000000000000000022-2-200
χ282222-2-22-2-22222222-2-22-2-22-2-2-2222-20000-220000000000000000000000000000-2-22200
χ292222-2-22-2-2-222-222222-2-2-2-222-222-2-22i2i−2i−2i2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ302222-2-22-2-2-222-222222-2-2-2-222-222-2-2−2i−2i2i2i2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ312222-2-2-1222-2-22-1-1-1-22-211-111-111-1-10000-11−i3−i3i3i3i3i3−i3−i32-2-1-10011−i3i3−i3i300000000000000
χ322222-2-2-1222-2-22-1-1-1-22-211-111-111-1-10000-11−i3−i3i3i3i3i3−i3−i3-221100-1-1i3−i3i3−i300000000000000
χ332222-2-2-1222-2-22-1-1-1-22-211-111-111-1-10000-11i3i3−i3−i3−i3−i3i3i32-2-1-10011i3−i3i3−i300000000000000
χ342222-2-2-1222-2-22-1-1-1-22-211-111-111-1-10000-11i3i3−i3−i3−i3−i3i3i3-221100-1-1−i3i3−i3i300000000000000
χ352222-2-2-1-2-2-222-2-1-1-122-2111-1-11-1-1112i2i−2i−2i-11−i−iii−i−iii00−i3i300i3−i33−3−3300000000000000
χ362222-2-2-1-2-2-222-2-1-1-122-2111-1-11-1-1112i2i−2i−2i-11−i−iii−i−iii00i3−i300−i3i3−333−300000000000000
χ372222-2-2-1-2-2-222-2-1-1-122-2111-1-11-1-111−2i−2i2i2i-11ii−i−iii−i−i00−i3i300i3−i3−333−300000000000000
χ382222-2-2-1-2-2-222-2-1-1-122-2111-1-11-1-111−2i−2i2i2i-11ii−i−iii−i−i00i3−i300−i3i33−3−3300000000000000
χ392-2-222-222-202-20-2-220002-200022-20-2−i2i2−i2i200−i2i2−i2i2−i2i2−i2i20000000000000000002i−2i2−22−200
χ402-2-222-222-202-20-2-220002-200022-20-2−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2000000000000000000−2i2i−22−2200
χ412-2-222-222-202-20-2-220002-200022-20-2i2−i2i2−i200i2−i2i2−i2i2−i2i2−i20000000000000000002i−2i−22−2200
χ422-2-222-222-202-20-2-220002-200022-20-2i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2000000000000000000−2i2i2−22−200
χ432-2-22-222-2202-20-2-22000-22000-22-2022−2−22002−2−222−2−2200000000000000002-2002−2−2200
χ442-2-22-222-2202-20-2-22000-22000-22-2022−2−22002−2−222−2−220000000000000000-2200−222−200
χ452-2-22-222-2202-20-2-22000-22000-22-202−222−200−222−2−222−200000000000000002-200−222−200
χ462-2-22-222-2202-20-2-22000-22000-22-202−222−200−222−2−222−20000000000000000-22002−2−2200
χ47444444-244-444-4-2-2-2-4-4-4-2-2222-2-2-22-20000220000000000000000000000000000000000
χ48444444-2-4-44-4-44-2-2-24-4-4-2-2-2-2-2222-220000220000000000000000000000000000000000
χ494444-4-4-244-4-4-4-4-2-2-24-44222-2-2-2222-200002-20000000000000000000000000000000000
χ504444-4-4-2-4-44444-2-2-2-4-4422-2222-2-2-2200002-20000000000000000000000000000000000
χ5144-4-400400400-44-4-400000400000-40000000000000000000000000002i−2i2i−2i0000000000
χ5244-4-400400400-44-4-400000400000-4000000000000000000000000000−2i2i−2i2i0000000000
χ5344-4-400400-40044-4-400000-40000040000000000000000000000000002-2-220000000000
χ5444-4-400400-40044-4-400000-4000004000000000000000000000000000-222-20000000000
χ554-4-444-44-440-440-4-440004-4000-4-44040000000000000000000000000000000000000000
χ564-4-444-4-24-404-4022-2000-22000-2-2202−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ574-4-444-4-24-404-4022-2000-22000-2-22022i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ584-4-444-4-2-440-44022-2000-2200022-20-2000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000
χ594-4-444-4-2-440-44022-2000-2200022-20-2000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000
χ604-4-44-4444-40-440-4-44000-440004-440-40000000000000000000000000000000000000000
χ614-4-44-44-24-40-44022-20002-2000-22-2020000006−6−66−666−600000000000000000000000000
χ624-4-44-44-24-40-44022-20002-2000-22-202000000−666−66−6−6600000000000000000000000000
χ634-4-44-44-2-4404-4022-20002-20002-220-222−22−222200−222−2−222−200000000000000000000000000
χ644-4-44-44-2-4404-4022-20002-20002-220-2−222222−22002−2−222−2−2200000000000000000000000000
χ6588-8-800-400800-8-44400000-400000400000000000000000000000000000000000000000
χ6688-8-800-400-8008-44400000400000-400000000000000000000000000000000000000000
χ678-88-8008000000-88-800000000000000000000000000000000000000000000000000000
χ688-88-800-40000004-4400000043−43000000000000000000000000000000000000000000000
χ698-88-800-40000004-44000000−4343000000000000000000000000000000000000000000000

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