Finite Group Databasebeta

← Group #10834021

Character table — Group #10834021

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444466666662244888812121212121212122244666666881212121224242424242424244444888844121212124444448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1
χ911111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111111-111-1-1-1-111-1-1-1-1-11
χ1011111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-111111-1
χ1111111111111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-11-1-111-1-1-1-111-1-11-1
χ1211111111111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-111-11
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1-111-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-11111-1-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11-111-1-1-1-1-1-11111-11
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111-111-1-11111-1-1-1-11-1
χ17222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-200002200000000000000000022-2-20000000000-2200000000
χ18222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-2000022000000000000000000-2-22200000000002-200000000
χ19222222222-2-2-2-22222222-2-2220000-2-22222-2-20000-2-200000000000000000022-2-200000000002-200000000
χ20222222222-2-2-2-22222222-2-2220000-2-22222-2-20000-2-2000000000000000000-2-2220000000000-2200000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2-2-2-1-11111221111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-1-1-1-11111111100000000-2-211110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-1-11111-2-21111111111110000000022-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-11111-1-122-2-211-1-1-1-1-2-21111-1-1-1-11111000000002-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-11111-1-1-2-222111111-2-2-1-1-1-1-1-1-1-1111100000000-2211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-122-2-211-1-1-1-12211111111-1-1-1-100000000-2211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1-2-22211111122-1-1-1-11111-1-1-1-1000000002-2-1-1110000000000
χ2922-22-22-2-222-22-22-2-2-22-22000000002-200002-22-2000022-2-2000000000000002i−2i2i−2i0000000000002i−2i000000
χ3022-22-22-2-222-22-22-2-2-22-22000000002-200002-22-2000022-2-200000000000000−2i2i−2i2i000000000000−2i2i000000
χ3122-22-22-2-222-22-22-2-2-22-22000000002-200002-2-220000-2-222000000000000002i−2i2i−2i000000000000−2i2i000000
χ3222-22-22-2-222-22-22-2-2-22-22000000002-200002-2-220000-2-22200000000000000−2i2i−2i2i0000000000002i−2i000000
χ3322-22-22-2-22-22-222-2-2-22-2200000000-220000-22002-20000000022-2-2000000002i−2i−2i2i000000000000002i−2i0000
χ3422-22-22-2-22-22-222-2-2-22-2200000000-220000-22002-20000000022-2-200000000−2i2i2i−2i00000000000000−2i2i0000
χ3522-22-22-2-22-22-222-2-2-22-2200000000-220000-2200-2200000000-2-222000000002i−2i−2i2i00000000000000−2i2i0000
χ3622-22-22-2-22-22-222-2-2-22-2200000000-220000-2200-2200000000-2-22200000000−2i2i2i−2i000000000000002i−2i0000
χ372-2-2-2222-2222-2-2-222-2-2-222-22-22i2i−2i−2i2222-2-2-2-200002-200002i−2i00002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ382-2-2-2222-2222-2-2-222-2-2-222-22-2−2i−2i2i2i2222-2-2-2-200002-20000−2i2i0000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ392-2-2-2222-2222-2-2-222-2-2-22-22-222i2i−2i−2i22-2-222-2-20000-220000−2i2i00002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ402-2-2-2222-2222-2-2-222-2-2-22-22-22−2i−2i2i2i22-2-222-2-20000-2200002i−2i0000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ412-2-2-2222-22-2-222-222-2-2-222-2-220000-2-2-2-2222200002-2000000000000000000000022-2-20000000000002-200
χ422-2-2-2222-22-2-222-222-2-2-222-2-220000-2-2-2-2222200002-20000000000000000000000-2-222000000000000-2200
χ432-2-2-2222-22-2-222-222-2-2-22-222-20000-2-222-2-2220000-22000000000000000000000022-2-2000000000000-2200
χ442-2-2-2222-22-2-222-222-2-2-22-222-20000-2-222-2-2220000-220000000000000000000000-2-2220000000000002-200
χ452-2-2-2222-2-122-2-21-1-1111-12-22-22i2i−2i−2i-1-1-1-111110000-11−i3i3−i3i32i−2i−i3i3−i3i3−i−iii−i−iii00000000003−33−30000000000
χ462-2-2-2222-2-122-2-21-1-1111-12-22-22i2i−2i−2i-1-1-1-111110000-11i3−i3i3−i32i−2ii3−i3i3−i3−i−iii−i−iii0000000000−33−330000000000
χ472-2-2-2222-2-122-2-21-1-1111-12-22-2−2i−2i2i2i-1-1-1-111110000-11−i3i3−i3i3−2i2i−i3i3−i3i3ii−i−iii−i−i0000000000−33−330000000000
χ482-2-2-2222-2-122-2-21-1-1111-12-22-2−2i−2i2i2i-1-1-1-111110000-11i3−i3i3−i3−2i2ii3−i3i3−i3ii−i−iii−i−i00000000003−33−30000000000
χ492-2-2-2222-2-122-2-21-1-1111-1-22-222i2i−2i−2i-1-111-1-11100001-1−i3i3−i3i3−2i2ii3−i3i3−i3−i−iiiii−i−i00000000003−3−330000000000
χ502-2-2-2222-2-122-2-21-1-1111-1-22-222i2i−2i−2i-1-111-1-11100001-1i3−i3i3−i3−2i2i−i3i3−i3i3−i−iiiii−i−i0000000000−333−30000000000
χ512-2-2-2222-2-122-2-21-1-1111-1-22-22−2i−2i2i2i-1-111-1-11100001-1−i3i3−i3i32i−2ii3−i3i3−i3ii−i−i−i−iii0000000000−333−30000000000
χ522-2-2-2222-2-122-2-21-1-1111-1-22-22−2i−2i2i2i-1-111-1-11100001-1i3−i3i3−i32i−2i−i3i3−i3i3ii−i−i−i−iii00000000003−3−330000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000222222220000-2-2000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444000022-2-2-2-222000022000000000000000000000000000000000000000000
χ55444-4-4-44-44000044-44-4-4-40000000000000000000000000000000000000000000022−2222−220000000000000000
χ56444-4-4-44-44000044-44-4-4-400000000000000000000000000000000000000000000−2222−22220000000000000000
χ5744-44-44-4-4-24-44-4-2222-22-200000000-220000-224-40000-2-22200000000000000000000000000000000000000
χ5844-44-44-4-4-24-44-4-2222-22-200000000-220000-22-44000022-2-200000000000000000000000000000000000000
χ5944-44-44-4-4-2-44-44-2222-22-2000000002-200002-2004-400000000-2-22200000000000000000000000000000000
χ6044-44-44-4-4-2-44-44-2222-22-2000000002-200002-200-440000000022-2-200000000000000000000000000000000
χ6144-4-44-4-44400004-44-4-44-40000−2i22i2−2i22i2000000000000000000000000−2i22i2−2i22i20000000000000000000000000000
χ6244-4-44-4-44400004-44-4-44-400002i2−2i22i2−2i20000000000000000000000002i2−2i22i2−2i20000000000000000000000000000
χ6344-4-44-4-44-20000-22-222-220000−2i22i2−2i22i20023−2323−23000000000000000000i2−i2i2−i2i6−i6i6−i6000000000000000000000000
χ6444-4-44-4-44-20000-22-222-220000−2i22i2−2i22i200−2323−2323000000000000000000i2−i2i2−i2−i6i6−i6i6000000000000000000000000
χ6544-4-44-4-44-20000-22-222-2200002i2−2i22i2−2i20023−2323−23000000000000000000−i2i2−i2i2−i6i6−i6i6000000000000000000000000
χ6644-4-44-4-44-20000-22-222-2200002i2−2i22i2−2i200−2323−2323000000000000000000−i2i2−i2i2i6−i6i6−i6000000000000000000000000
χ674-4444-4-4-440000-4-4444-4-4000022−22−222200000000000000000000000022−22−22220000000000000000000000000000
χ684-4444-4-4-440000-4-4444-4-40000−222222−22000000000000000000000000−222222−220000000000000000000000000000
χ694-4444-4-4-4-2000022-2-2-222000022−22−22220023−23−2323000000000000000000−222−2−666−6000000000000000000000000
χ704-4444-4-4-4-2000022-2-2-222000022−22−222200−232323−23000000000000000000−222−26−6−66000000000000000000000000
χ714-4444-4-4-4-2000022-2-2-2220000−222222−220023−23−23230000000000000000002−2−226−6−66000000000000000000000000
χ724-4444-4-4-4-2000022-2-2-2220000−222222−2200−232323−230000000000000000002−2−22−666−6000000000000000000000000
χ734-44-4-44-4444-4-44-4-4-44-444000000004-40000-44000000000000000000000000000000000000000000000000
χ744-44-4-44-444-444-4-4-4-44-44400000000-4400004-4000000000000000000000000000000000000000000000000
χ754-44-4-44-44-24-4-44222-22-2-200000000-2200002-2000000−2i32i32i3−2i300000000000000000000000000000000000000
χ764-44-4-44-44-24-4-44222-22-2-200000000-2200002-20000002i3−2i3−2i32i300000000000000000000000000000000000000
χ774-44-4-44-44-2-444-4222-22-2-2000000002-20000-22000000000000−2i32i32i3−2i300000000000000000000000000000000
χ784-44-4-44-44-2-444-4222-22-2-2000000002-20000-220000000000002i3−2i3−2i32i300000000000000000000000000000000
χ794-4-44-4-44440000-44-4-444-40000000000000000000000000000000000000000000022−22−22220000000000000000
χ804-4-44-4-44440000-44-4-444-400000000000000000000000000000000000000000000−222222−220000000000000000
χ814-4-4-4444-4-2-4-4442-2-2222-24-4-4400002222-2-2-2-20000-22000000000000000000000000000000000000000000
χ824-4-4-4444-4-2-4-4442-2-2222-2-444-4000022-2-222-2-200002-2000000000000000000000000000000000000000000
χ83888-8-8-88-8-40000-4-44-44440000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-8-888-400004-444-4-440000000000000000000000000000000000000000000000000000000000000000

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