Finite Group Databasebeta

← Group #10827369

Character table — Group #10827369

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order12222222344446666666224444666688881212121244444444488121212121212121212122424242424242424224488884121212122222444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1111-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1111
χ51111111111111111111111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-11
χ81111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-11111-1
χ911111111111111111111-1-11111-1-1-1-1111111111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-111-1-111-111-1-1-1
χ1011111111111111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-11-1-1111
χ1111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-1-1-1-111111
χ1211111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1111111111-1-111111-1-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111111-1-111-1-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-11111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1111111-1-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-111-1-1-1-1111-1-11
χ17222222222-2-2-2-2222222222000022220000-2-2-2-22222-2000000-2-20000000000000000-2-2220000000000000-200000
χ18222222222-2-2-2-2222222222000022220000-2-2-2-2-2-2-2-2-2000000-2-2000000000000000022-2-20000000000000200000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-20000-2-2-2-222222000000220000000000000000-2-2-2-20000000000000200000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-20000-2-2-2-2-2-2-2-2200000022000000000000000022220000000000000-200000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-100002222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-10000222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-12222-1-1-1-100002-2-2-2-222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-2-2-2-2-1-1-1-100002-2-222-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2222211112222-1-1-1-10000-2-2-222-2-211-1-1-1-11111-1-1-1-1111100000000-211-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222221111-2-2-2-2-1-1-1-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-1000000002-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-211112222-1-1-1-10000-222-2-2-2-2111111-1-1-1-1-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-2-2-2-2-1-1-1-10000-2222222111111-1-1-1-11111-1-1-1-100000000-211-1-10000000000
χ2922-22-22-2-222-22-22-2-2-222-2002i2i−2i−2i00002i2i−2i−2i22-2-200000002-200002i2i−2i−2i00002i2i−2i−2i0000000000000002-20000000000
χ3022-22-22-2-222-22-22-2-2-222-2002i2i−2i−2i0000−2i−2i2i2i22-2-20000000-2200002i2i−2i−2i0000−2i−2i2i2i000000000000000-220000000000
χ3122-22-22-2-222-22-22-2-2-222-200−2i−2i2i2i00002i2i−2i−2i22-2-20000000-220000−2i−2i2i2i00002i2i−2i−2i000000000000000-220000000000
χ3222-22-22-2-222-22-22-2-2-222-200−2i−2i2i2i0000−2i−2i2i2i22-2-200000002-20000−2i−2i2i2i0000−2i−2i2i2i0000000000000002-20000000000
χ3322-22-22-2-2-12-22-2-1111-1-11002i2i−2i−2i−i3−i3i3i32i2i−2i−2i-1-11100000002-200−i3i3−i−iii33−3−3−i−iii33−3−3000000000−i3i3-110000000000
χ3422-22-22-2-2-12-22-2-1111-1-11002i2i−2i−2i−i3−i3i3i3−2i−2i2i2i-1-1110000000-2200−i3i3−i−iii33−3−3ii−i−i−3−333000000000i3−i31-10000000000
χ3522-22-22-2-2-12-22-2-1111-1-11002i2i−2i−2ii3i3−i3−i32i2i−2i−2i-1-11100000002-200i3−i3−i−iii−3−333−i−iii−3−333000000000i3−i3-110000000000
χ3622-22-22-2-2-12-22-2-1111-1-11002i2i−2i−2ii3i3−i3−i3−2i−2i2i2i-1-1110000000-2200i3−i3−i−iii−3−333ii−i−i33−3−3000000000−i3i31-10000000000
χ3722-22-22-2-2-12-22-2-1111-1-1100−2i−2i2i2i−i3−i3i3i32i2i−2i−2i-1-1110000000-2200−i3i3ii−i−i−3−333−i−iii33−3−3000000000i3−i31-10000000000
χ3822-22-22-2-2-12-22-2-1111-1-1100−2i−2i2i2i−i3−i3i3i3−2i−2i2i2i-1-11100000002-200−i3i3ii−i−i−3−333ii−i−i−3−333000000000−i3i3-110000000000
χ3922-22-22-2-2-12-22-2-1111-1-1100−2i−2i2i2ii3i3−i3−i32i2i−2i−2i-1-1110000000-2200i3−i3ii−i−i33−3−3−i−iii−3−333000000000−i3i31-10000000000
χ4022-22-22-2-2-12-22-2-1111-1-1100−2i−2i2i2ii3i3−i3−i3−2i−2i2i2i-1-11100000002-200i3−i3ii−i−i33−3−3ii−i−i33−3−3000000000i3−i3-110000000000
χ4122-2-22-2-2220000222-2-2-2-22-200002-22-22−22−200002i2i−2i−2i000002−200000000002−22−22−22−2002i−2i−i2−i2i2i2000000000000−i2i20
χ4222-2-22-2-2220000222-2-2-2-22-200002-22-22−22−20000−2i−2i2i2i000002−200000000002−22−22−22−200−2i2ii2i2−i2−i2000000000000i2−i20
χ4322-2-22-2-2220000222-2-2-2-22-200002-22-2−22−2200002i2i−2i−2i00000−220000000000−22−22−22−22002i−2ii2i2−i2−i2000000000000i2−i20
χ4422-2-22-2-2220000222-2-2-2-22-200002-22-2−22−220000−2i−2i2i2i00000−220000000000−22−22−22−2200−2i2i−i2−i2i2i2000000000000−i2i20
χ4522-2-22-2-2220000222-2-2-2-2-220000-22-222−22−200002i2i−2i−2i00000−2200000000002−22−2−22−2200−2i2i−i2−i2i2i2000000000000i2−i20
χ4622-2-22-2-2220000222-2-2-2-2-220000-22-222−22−20000−2i−2i2i2i00000−2200000000002−22−2−22−22002i−2ii2i2−i2−i2000000000000−i2i20
χ4722-2-22-2-2220000222-2-2-2-2-220000-22-22−22−2200002i2i−2i−2i000002−20000000000−22−222−22−200−2i2ii2i2−i2−i2000000000000−i2i20
χ4822-2-22-2-2220000222-2-2-2-2-220000-22-22−22−220000−2i−2i2i2i000002−20000000000−22−222−22−2002i−2i−i2−i2i2i2000000000000i2−i20
χ492-22-222-2-2222-2-2-22-22-22-2002i−2i2i−2i000000002-22-200000000000002i−2i2i−2i00000000000000002i−2i2i−2i00000002-2000000
χ502-22-222-2-2222-2-2-22-22-22-2002i−2i2i−2i000000002-22-200000000000002i−2i2i−2i0000000000000000−2i2i−2i2i0000000-22000000
χ512-22-222-2-2222-2-2-22-22-22-200−2i2i−2i2i000000002-22-20000000000000−2i2i−2i2i00000000000000002i−2i2i−2i0000000-22000000
χ522-22-222-2-2222-2-2-22-22-22-200−2i2i−2i2i000000002-22-20000000000000−2i2i−2i2i0000000000000000−2i2i−2i2i00000002-2000000
χ532-2-2-2-222222-2-22-2-22-2-222002-2-22000000002-2-222-22-20000000002-2-220000000000002-200000000000000002-2000
χ542-2-2-2-222222-2-22-2-22-2-222002-2-22000000002-2-22-22-220000000002-2-22000000000000-220000000000000000-22000
χ552-2-2-2-222222-2-22-2-22-2-22200-222-2000000002-2-222-22-2000000000-222-20000000000002-20000000000000000-22000
χ562-2-2-2-222222-2-22-2-22-2-22200-222-2000000002-2-22-22-22000000000-222-2000000000000-2200000000000000002-2000
χ572-2-2-2-22222-222-2-2-22-2-22200000000000000-222-22-22-202-200000000002-22-200000000-22000000000002-200000000
χ582-2-2-2-22222-222-2-2-22-2-22200000000000000-222-22-22-20-220000000000-22-2200000000-2200000000000-2200000000
χ592-2-2-2-22222-222-2-2-22-2-22200000000000000-222-2-22-2202-200000000002-22-2000000002-200000000000-2200000000
χ602-2-2-2-22222-222-2-2-22-2-22200000000000000-222-2-22-220-220000000000-22-22000000002-2000000000002-200000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2440000-2-2-2-2000022220000-400000022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022220000222200004000000-2-2000000000000000000000000000000000000000
χ63444-4-4-44-4400004-4-44-4-440000000000−2i22i22i2−2i20000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ64444-4-4-44-4400004-4-44-4-4400000000002i2−2i2−2i22i200000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ65444-4-4-44-4-20000-222-222-2000000−2i32i32i3−2i3−2i22i22i2−2i20000000000000000000000000i2−i2−i2i2−666−600000000000000000000000
χ66444-4-4-44-4-20000-222-222-2000000−2i32i32i3−2i32i2−2i2−2i22i20000000000000000000000000−i2i2i2−i26−6−6600000000000000000000000
χ67444-4-4-44-4-20000-222-222-20000002i3−2i3−2i32i3−2i22i22i2−2i20000000000000000000000000i2−i2−i2i26−6−6600000000000000000000000
χ68444-4-4-44-4-20000-222-222-20000002i3−2i3−2i32i32i2−2i2−2i22i20000000000000000000000000−i2i2i2−i2−666−600000000000000000000000
χ6944-44-44-4-44-44-444-4-4-444-400000000000000-4-4440000000000000000000000000000000000000000000000000000
χ7044-44-44-4-4-2-44-44-2222-2-22000000−2i3−2i32i32i3000022-2-2000000000002i3−2i3000000000000000000000000000000000000000
χ7144-44-44-4-4-2-44-44-2222-2-220000002i32i3−2i3−2i3000022-2-200000000000−2i32i3000000000000000000000000000000000000000
χ7244-4-44-4-44-20000-2-2-222224-40000-22-2222−2222−22000000000000022−220000000000−22−22−22−2200000000000000000000000
χ7344-4-44-4-44-20000-2-2-222224-40000-22-22−2222−22220000000000000−222200000000002−22−22−22−200000000000000000000000
χ7444-4-44-4-44-20000-2-2-22222-4400002-22-222−2222−220000000000000−22220000000000−22−222−22−200000000000000000000000
χ7544-4-44-4-44-20000-2-2-22222-4400002-22-2−2222−2222000000000000022−2200000000002−22−2−22−2200000000000000000000000
χ764-444-4-4-4440000-4-4444-4-40000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ774-444-4-4-4440000-4-4444-4-4000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ784-44-444-4-44-4-444-44-44-44-400000000000000-44-440000000000000000000000000000000000000000000000000000
χ794-44-444-4-4-244-4-42-22-22-22004i−4i4i−4i00000000-22-220000000000000−2i2i−2i2i00000000000000000000000000000000000
χ804-44-444-4-4-244-4-42-22-22-2200−4i4i−4i4i00000000-22-2200000000000002i−2i2i−2i00000000000000000000000000000000000
χ814-44-444-4-4-2-4-4442-22-22-22000000000000002-22-20000000000000000023−23−23230000000000000000000000000000000
χ824-44-444-4-4-2-4-4442-22-22-22000000000000002-22-200000000000000000−232323−230000000000000000000000000000000
χ834-4-444-44-440000-44-4-44-4400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ844-4-444-44-440000-44-4-44-44000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ854-4-4-4-4444-24-4-4422-222-2-2004-4-4400000000-222-20000000000000-222-200000000000000000000000000000000000
χ864-4-4-4-4444-24-4-4422-222-2-200-444-400000000-222-200000000000002-2-2200000000000000000000000000000000000
χ874-4-4-4-4444-2-444-422-222-2-2000000000000002-2-22000004-40000000000-22-220000000000000000000000000000000
χ884-4-4-4-4444-2-444-422-222-2-2000000000000002-2-2200000-4400000000002-22-20000000000000000000000000000000
χ898-888-8-8-88-4000044-4-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-88-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000

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