Finite Group Databasebeta

← Group #10858807

Character table — Group #10858807

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order1222222234444444466666662244444444121212121212121212121212121212121212121212121212444444446612121212121212121212121212121212888888884444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-11-1-11-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-11-1-11-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-111-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ911111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-11
χ1011111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-11-1
χ1111111111111-1-1-1-1111111111-1-11111-1-111111111111111-1-1-1-11111-1-1-1-111-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1211111111111-1-1-1-1111111111-1-11111-1-111111111111111-1-1-1-11111-1-1-1-111-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1311111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ1411111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ1511111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1-11
χ1611111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1111-1
χ17222222222-2-22222-2-22222222-2-2000022222222000000002222-2-2-2-2222200-200-200-2-2-2-200000000-2-20000000000000000000000
χ18222222222-2-22222-2-22222222-2-20000-2-2-2-2-2-2-2-200000000-2-2-2-2-2-2-2-2222200200200-2-22200000000220000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222000022-2-2-2-2-2-2000000002222-2-2-2-2-2-2-2-200-200200222200000000-2-20000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222220000-2-222222200000000-2-2-2-2-2-2-2-2-2-2-2-200200-20022-2-200000000220000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-2-2-2-21111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1111111-1-1-1-1111111000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-2-22-2-22-2-2-1-1-1-111111111-1-11111000000000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-122-222-2-2-2-1-111-1-1-1-1111111-1-1-1-1000000000000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2222222-2-21111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-2222-2-2-2111111111111-1-1-1-1-1-1000000000000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-22222-2-222-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111122-2-2-22-2-211-1-1-1-1-1-11111111111000000000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-2111111111111-1-1-1-1-1-1-1-11111222-2-2-2221111-1-1-1-1-1-1-1-1-1-11111000000000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1111111111111-1-1-1-11111-2-2-22222211-1-11111-1-1-1-111-1-1-1-1000000000000000000
χ2922222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-200002222-1-1-1-1−i3−i3−i3−i3i3i3i3i3-1-1-1-11111-1-1-1-100-200-2001111−i3−i3i3i3−i3−i3i3i311−i3−i3i3i3000000000000000000
χ3022222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-200002222-1-1-1-1i3i3i3i3−i3−i3−i3−i3-1-1-1-11111-1-1-1-100-200-2001111i3i3−i3−i3i3i3−i3−i311i3i3−i3−i3000000000000000000
χ3122222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-20000-2-2-2-21111−i3−i3−i3−i3i3i3i3i311111111-1-1-1-10020020011-1-1i3i3−i3−i3−i3−i3i3i3-1-1i3i3−i3−i3000000000000000000
χ3222222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-20000-2-2-2-21111i3i3i3i3−i3−i3−i3−i311111111-1-1-1-10020020011-1-1−i3−i3i3i3i3i3−i3−i3-1-1−i3−i3i3i3000000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122000022-2-21111−i3−i3−i3−i3i3i3i3i3-1-1-1-11111111100-200200-1-1-1-1i3i3−i3−i3i3i3−i3−i311−i3−i3i3i3000000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122000022-2-21111i3i3i3i3−i3−i3−i3−i3-1-1-1-11111111100-200200-1-1-1-1−i3−i3i3i3−i3−i3i3i311i3i3−i3−i3000000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000-2-222-1-1-1-1−i3−i3−i3−i3i3i3i3i311111111111100200-200-1-111−i3−i3i3i3i3i3−i3−i3-1-1i3i3−i3−i3000000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000-2-222-1-1-1-1i3i3i3i3−i3−i3−i3−i311111111111100200-200-1-111i3i3−i3−i3−i3−i3i3i3-1-1−i3−i3i3i3000000000000000000
χ37222-22-2-2-222222-2-2-2-22-2-22-2-222-200000000000000000000000022-2-222-2-22-202-20002-2002-22-20000002-22-2000000000000000000
χ38222-22-2-2-222222-2-2-2-22-2-22-2-222-200000000000000000000000022-2-222-2-2-220-220002-200-22-22000000-22-22000000000000000000
χ39222-22-2-2-2222-2-222-2-22-2-22-2-22-2200000000000000000000000022-2-2-2-2222-20-22000-22002-22-2000000-22-22000000000000000000
χ40222-22-2-2-2222-2-222-2-22-2-22-2-22-2200000000000000000000000022-2-2-2-222-2202-2000-2200-22-220000002-22-2000000000000000000
χ41222-22-2-2-22-2-222-2-2222-2-22-2-22-222i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i0000-2-22222-2-20000002i−2i-220000002i−2i2i−2i000000000000000000000000
χ42222-22-2-2-22-2-222-2-2222-2-22-2-22-22−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i0000-2-22222-2-2000000−2i2i-22000000−2i2i−2i2i000000000000000000000000
χ43222-22-2-2-22-2-2-2-222222-2-22-2-222-22i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i0000-2-222-2-222000000−2i2i2-2000000−2i2i−2i2i000000000000000000000000
χ44222-22-2-2-22-2-2-2-222222-2-22-2-222-2−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i0000-2-222-2-2220000002i−2i2-20000002i−2i2i−2i000000000000000000000000
χ45222-22-2-2-2-12222-2-2-2-2-111-111-12-20000000033−3−333−3−3−3−33333−3−3-1-111-1-1112-202-2000-113−3-11-113−3−333−3-11-11000000000000000000
χ46222-22-2-2-2-12222-2-2-2-2-111-111-12-20000000033−3−3−3−33333−3−333−3−3-1-111-1-111-220-22000-113−31-11-1−333−33−31-11-1000000000000000000
χ47222-22-2-2-2-12222-2-2-2-2-111-111-12-200000000−3−33333−3−3−3−333−3−333-1-111-1-111-220-22000-11−331-11-13−3−33−331-11-1000000000000000000
χ48222-22-2-2-2-12222-2-2-2-2-111-111-12-200000000−3−333−3−33333−3−3−3−333-1-111-1-1112-202-2000-11−33-11-11−333−3−33-11-11000000000000000000
χ49222-22-2-2-2-122-2-222-2-2-111-111-1-220000000033−3−333−3−3−3−333−3−333-1-11111-1-12-20-220001-13−3-11-11−333−3−331-11-1000000000000000000
χ50222-22-2-2-2-122-2-222-2-2-111-111-1-220000000033−3−3−3−33333−3−3−3−333-1-11111-1-1-2202-20001-13−31-11-13−3−33−33-11-11000000000000000000
χ51222-22-2-2-2-122-2-222-2-2-111-111-1-2200000000−3−33333−3−3−3−33333−3−3-1-11111-1-1-2202-20001-1−331-11-1−333−33−3-11-11000000000000000000
χ52222-22-2-2-2-122-2-222-2-2-111-111-1-2200000000−3−333−3−33333−3−333−3−3-1-11111-1-12-20-220001-1−33-11-113−3−333−31-11-1000000000000000000
χ53222-22-2-2-2-1-2-222-2-222-111-111-1-222i2i−2i−2i000033−3−3−i−iii−i−iii33−3−311-1-1-1-1110000002i−2i1-1−33−i3i3i3−i3−ii−ii−33−i3i3i3−i3000000000000000000
χ54222-22-2-2-2-1-2-222-2-222-111-111-1-222i2i−2i−2i0000−3−333−i−iii−i−iii−3−33311-1-1-1-1110000002i−2i1-13−3i3−i3−i3i3−ii−ii3−3i3−i3−i3i3000000000000000000
χ55222-22-2-2-2-1-2-222-2-222-111-111-1-22−2i−2i2i2i000033−3−3ii−i−iii−i−i33−3−311-1-1-1-111000000−2i2i1-1−33i3−i3−i3i3i−ii−i−33i3−i3−i3i3000000000000000000
χ56222-22-2-2-2-1-2-222-2-222-111-111-1-22−2i−2i2i2i0000−3−333ii−i−iii−i−i−3−33311-1-1-1-111000000−2i2i1-13−3−i3i3i3−i3i−ii−i3−3−i3i3i3−i3000000000000000000
χ57222-22-2-2-2-1-2-2-2-22222-111-111-12-22i2i−2i−2i000033−3−3−i−iii−i−iii−3−33311-1-111-1-1000000−2i2i-11−33−i3i3i3−i3i−ii−i3−3i3−i3−i3i3000000000000000000
χ58222-22-2-2-2-1-2-2-2-22222-111-111-12-22i2i−2i−2i0000−3−333−i−iii−i−iii33−3−311-1-111-1-1000000−2i2i-113−3i3−i3−i3i3i−ii−i−33−i3i3i3−i3000000000000000000
χ59222-22-2-2-2-1-2-2-2-22222-111-111-12-2−2i−2i2i2i000033−3−3ii−i−iii−i−i−3−33311-1-111-1-10000002i−2i-11−33i3−i3−i3i3−ii−ii3−3−i3i3i3−i3000000000000000000
χ60222-22-2-2-2-1-2-2-2-22222-111-111-12-2−2i−2i2i2i0000−3−333ii−i−iii−i−i33−3−311-1-111-1-10000002i−2i-113−3−i3i3i3−i3−ii−ii−33i3−i3−i3i3000000000000000000
χ612-222-2-2-222002i−2i2i−2i00-22-222-2-20000002i−2i2-22-22-2000000002i−2i2i−2i00002i−2i2i−2i00000000000000000000000000−i2−i2i2i222−2−20000−i2i22−200
χ622-222-2-2-222002i−2i2i−2i00-22-222-2-20000002i−2i2-22-22-2000000002i−2i2i−2i00002i−2i2i−2i00000000000000000000000000i2i2−i2−i2−2−2220000i2−i2−2200
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χ652-222-2-2-22200−2i2i−2i2i00-22-222-2-20000002i−2i-22-22-22000000002i−2i2i−2i0000−2i2i−2i2i00000000000000000000000000−i2−i2i2i2−2−2220000i2−i22−200
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χ924-4-444-44-4-24-400004-42222-2-2-2004-44-400000000-22-22-22-220000-22-22000000000000000000000000000000000000000000000000
χ934-4-444-44-4-24-400004-42222-2-2-200-44-44000000002-22-22-22-20000-22-22000000000000000000000000000000000000000000000000
χ944-4-444-44-4-2-440000-442222-2-2-200000000000000−2i32i3−2i32i32i3−2i32i3−2i300002-22-2000000000000000000000000000000000000000000000000
χ954-4-444-44-4-2-440000-442222-2-2-2000000000000002i3−2i32i3−2i3−2i32i3−2i32i300002-22-2000000000000000000000000000000000000000000000000
χ964-4-4-444-4444-40000-44-444-4-4-44000000000000000000000000004-4-44000000000000000000000000000000000000000000000000
χ974-4-4-444-44-24-40000-442-2-2222-20000000000000023−23−2323−232323−230000-222-2000000000000000000000000000000000000000000000000
χ984-4-4-444-44-24-40000-442-2-2222-200000000000000−232323−2323−23−23230000-222-2000000000000000000000000000000000000000000000000
χ994-4-4-444-44-2-4400004-42-2-2222-2004i−4i−4i4i00000000−2i2i2i−2i−2i2i2i−2i00002-2-22000000000000000000000000000000000000000000000000
χ1004-4-4-444-44-2-4400004-42-2-2222-200−4i4i4i−4i000000002i−2i−2i2i2i−2i−2i2i00002-2-22000000000000000000000000000000000000000000000000
χ10188-88-88-8-8-400000000-44-44-444000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-8-888-400000000-4-4444-44000000000000000000000000000000000000000000000000000000000000000000000000000000

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