Finite Group Databasebeta

← Group #10830999

Character table — Group #10830999

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121212121216161616161624242424242424244848
order12222222344446666666224466668888121212124444881212121212121212121224242424242424244444888844121212122224448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11-1-11-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111
χ51111111111111111111111111111-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111
χ61111111111111111111111111111-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-11111-1-1
χ71111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111
χ911111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111-111-1-1-111-1-1-1-1-11-1
χ1011111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-1-111111-11
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-11-1-111-1-1-1-111-1-1-11
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1111-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1-1-1-111111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1111111-1-1-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-111-1-1-111-1-1-111-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-111-1-11-1-1111-1-11-1
χ17222222222-2-2-2-2222222222-2-222220000-2-2-2-2000000-2-2000000000000000022-2-20000000000200-2000000
χ18222222222-2-2-2-2222222222-2-222220000-2-2-2-2000000-2-20000000000000000-2-2220000000000-2002000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-20000-2-2-2-200000022000000000000000022-2-20000000000-2002000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-20000-2-2-2-2000000220000000000000000-2-2220000000000200-2000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-2-2-2-222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-211112222-1-1-1-122-2-2-2-211-1-1-1-11111-1-1-1-11111000000002-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-211112222-1-1-1-1-2-222-2-2111111-1-1-1-1-1-1-1-1111100000000-2211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-1-1-122-2-22211-1-1-1-111111111-1-1-1-100000000-2211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-1-1-1-2-22222111111-1-1-1-11111-1-1-1-1000000002-2-1-1110000000000
χ2922-2-2-2-22222-2-222-2-2-22-220000000000002-22-22-200000022-2-2000000000000000022-2-200000002-20000000
χ3022-2-2-2-22222-2-222-2-2-22-220000000000002-22-22-200000022-2-20000000000000000-2-2220000000-220000000
χ3122-2-2-2-22222-2-222-2-2-22-220000000000002-22-2-22000000-2-222000000000000000022-2-20000000-220000000
χ3222-2-2-2-22222-2-222-2-2-22-220000000000002-22-2-22000000-2-2220000000000000000-2-22200000002-20000000
χ332-22-2-22-222-22-22-22-2-2-222000000000000-222-2002-20000000022-2-20000000000002-22-200000000002-20000
χ342-22-2-22-222-22-22-22-2-2-222000000000000-222-2002-20000000022-2-2000000000000-22-220000000000-220000
χ352-22-2-22-222-22-22-22-2-2-222000000000000-222-200-2200000000-2-2220000000000002-22-20000000000-220000
χ362-22-2-22-222-22-22-22-2-2-222000000000000-222-200-2200000000-2-222000000000000-22-2200000000002-20000
χ372-2-222-2-22222-2-2-2-222-2-222-22-222-2-22i2i−2i−2i22-2-200002i−2i2-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ382-2-222-2-22222-2-2-2-222-2-222-22-222-2-2−2i−2i2i2i22-2-20000−2i2i2-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ392-2-222-2-22222-2-2-2-222-2-22-22-22-2-2222i2i−2i−2i22-2-20000−2i2i-22000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ402-2-222-2-22222-2-2-2-222-2-22-22-22-2-222−2i−2i2i2i22-2-200002i−2i-2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ412-2-222-2-222-2-222-2-222-2-222-2-2222-2-20000-2-222000000-22000000000000000000002-2-220000000000002-200
χ422-2-222-2-222-2-222-2-222-2-222-2-2222-2-20000-2-222000000-2200000000000000000000-222-2000000000000-2200
χ432-2-222-2-222-2-222-2-222-2-22-222-2-2-2220000-2-2220000002-2000000000000000000002-2-22000000000000-2200
χ442-2-222-2-222-2-222-2-222-2-22-222-2-2-2220000-2-2220000002-200000000000000000000-222-20000000000002-200
χ452-2-222-2-22-122-2-211-1-111-12-22-2-1-1112i2i−2i−2i-1-11100002i−2i-11−i3i3−i3i3−i3i3−i3i3−i−iii−i−iii00000000003−33−30000000000
χ462-2-222-2-22-122-2-211-1-111-12-22-2-1-1112i2i−2i−2i-1-11100002i−2i-11i3−i3i3−i3i3−i3i3−i3−i−iii−i−iii0000000000−33−330000000000
χ472-2-222-2-22-122-2-211-1-111-12-22-2-1-111−2i−2i2i2i-1-1110000−2i2i-11−i3i3−i3i3−i3i3−i3i3ii−i−iii−i−i0000000000−33−330000000000
χ482-2-222-2-22-122-2-211-1-111-12-22-2-1-111−2i−2i2i2i-1-1110000−2i2i-11i3−i3i3−i3i3−i3i3−i3ii−i−iii−i−i00000000003−33−30000000000
χ492-2-222-2-22-122-2-211-1-111-1-22-2211-1-12i2i−2i−2i-1-1110000−2i2i1-1−i3i3−i3i3i3−i3i3−i3−i−iiiii−i−i00000000003−3−330000000000
χ502-2-222-2-22-122-2-211-1-111-1-22-2211-1-12i2i−2i−2i-1-1110000−2i2i1-1i3−i3i3−i3−i3i3−i3i3−i−iiiii−i−i0000000000−333−30000000000
χ512-2-222-2-22-122-2-211-1-111-1-22-2211-1-1−2i−2i2i2i-1-11100002i−2i1-1−i3i3−i3i3i3−i3i3−i3ii−i−i−i−iii0000000000−333−30000000000
χ522-2-222-2-22-122-2-211-1-111-1-22-2211-1-1−2i−2i2i2i-1-11100002i−2i1-1i3−i3i3−i3−i3i3−i3i3ii−i−i−i−iii00000000003−3−330000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4-2-2-2-200002222000000220000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444222200002222000000-2-20000000000000000000000000000000000000000
χ554444-4-4-4-4400004-44-4-44-400000000000000000000000000000000000000004-40000000000000000000000
χ564444-4-4-4-4400004-44-4-44-40000000000000000000000000000000000000000-440000000000000000000000
χ5744-4-444-4-44000044-44-4-4-40000000022−2222−220000000000000000000022−2222−220000000000000000000000000000
χ5844-4-444-4-44000044-44-4-4-400000000−2222−222200000000000000000000−2222−22220000000000000000000000000000
χ5944-4-444-4-4-20000-2-22-22220000−2i32i3−2i32i322−2222−2200000000000000000000−22−22i6−i6i6−i6000000000000000000000000
χ6044-4-444-4-4-20000-2-22-22220000−2i32i3−2i32i3−2222−2222000000000000000000002−22−2−i6i6−i6i6000000000000000000000000
χ6144-4-444-4-4-20000-2-22-222200002i3−2i32i3−2i322−2222−2200000000000000000000−22−22−i6i6−i6i6000000000000000000000000
χ6244-4-444-4-4-20000-2-22-222200002i3−2i32i3−2i3−2222−2222000000000000000000002−22−2i6−i6i6−i6000000000000000000000000
χ6344-4-4-4-4444-444-44-4-4-44-44000000000000-44-44000000000000000000000000000000000000000000000000
χ6444-4-4-4-444-24-4-44-2222-22-2000000000000-22-224-4000000-2-222000000000000000000000000000000000000
χ6544-4-4-4-444-24-4-44-2222-22-2000000000000-22-22-4400000022-2-2000000000000000000000000000000000000
χ6644-4-4-4-444-2-444-4-2222-22-20000000000002-22-2000000000000−2i32i32i3−2i300000000000000000000000000000000
χ6744-4-4-4-444-2-444-4-2222-22-20000000000002-22-20000000000002i3−2i3−2i32i300000000000000000000000000000000
χ684-44-44-44-440000-4-4-4444-400000000−2i22i22i2−2i200000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ694-44-44-44-440000-4-4-4444-4000000002i2−2i2−2i22i2000000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ704-44-44-44-4-20000222-2-2-220000−2i32i32i3−2i3−2i22i22i2−2i200000000000000000000i2−i2−i2i26−6−66000000000000000000000000
χ714-44-44-44-4-20000222-2-2-220000−2i32i32i3−2i32i2−2i2−2i22i200000000000000000000−i2i2i2−i2−666−6000000000000000000000000
χ724-44-44-44-4-20000222-2-2-2200002i3−2i3−2i32i3−2i22i22i2−2i200000000000000000000i2−i2−i2i2−666−6000000000000000000000000
χ734-44-44-44-4-20000222-2-2-2200002i3−2i3−2i32i32i2−2i2−2i22i200000000000000000000−i2i2i2−i26−6−66000000000000000000000000
χ744-44-4-44-4444-44-4-44-4-4-4440000000000004-4-44000000000000000000000000000000000000000000000000
χ754-44-4-44-44-24-44-42-2222-2-2000000000000-222-200000000−2i32i32i3−2i3000000000000000000000000000000000000
χ764-44-4-44-44-24-44-42-2222-2-2000000000000-222-2000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ774-44-4-44-44-2-44-442-2222-2-20000000000002-2-22004-400000000-2-22200000000000000000000000000000000
χ784-44-4-44-44-2-44-442-2222-2-20000000000002-2-2200-440000000022-2-200000000000000000000000000000000
χ794-4-444-4-44-2-4-44422-2-222-24-4-44-2-222000022-2-20000002-20000000000000000000000000000000000000000
χ804-4-444-4-44-2-4-44422-2-222-2-444-422-2-2000022-2-2000000-220000000000000000000000000000000000000000
χ814-4-44-444-440000-444-44-4-40000000000000000000000000000000000000000004i−4i00000000000000000000
χ824-4-44-444-440000-444-44-4-4000000000000000000000000000000000000000000−4i4i00000000000000000000
χ838888-8-8-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-888-8-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000

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