Finite Group Databasebeta

← Group #10833985

Character table — Group #10833985

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121212121216161616161624242424242424244848
order12222222344446666666224466668888121212124444881212121212121212121224242424242424244444888844121212122244448824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-1111-1-1
χ4111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-111
χ51111111111111111111111111111-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ61111111111111111111111111111-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-11-1-111
χ81111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111-111-1-1-1-1-111-1-1-1-11
χ1011111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1111-1-11111-1
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-11-1-11111-1-1-1-1-1-11-1
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111111-11
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1-1-111-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-111111-1-11-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-111-1-111-1-1-1-111-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-111-1-1-1-11111-1-11-1
χ17222222222-2-2-2-2222222222-2-222220000-2-2-2-2000000-2-2000000000000000022-2-2000000000000-20020000
χ18222222222-2-2-2-2222222222-2-222220000-2-2-2-2000000-2-20000000000000000-2-222000000000000200-20000
χ19222222222-2-2-2-22222222-2-222-2-2-2-20000-2-2-2-200000022000000000000000022-2-2000000000000200-20000
χ20222222222-2-2-2-22222222-2-222-2-2-2-20000-2-2-2-2000000220000000000000000-2-222000000000000-20020000
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
χ2922-22-2-22-222-22-22-2-2-222-20000000000002-22-2002i−2i000000002i2i−2i−2i000000002i−2i2i−2i00000000002-200000000
χ3022-22-2-22-222-22-22-2-2-222-20000000000002-22-2002i−2i000000002i2i−2i−2i00000000−2i2i−2i2i0000000000-2200000000
χ3122-22-2-22-222-22-22-2-2-222-20000000000002-22-200−2i2i00000000−2i−2i2i2i000000002i−2i2i−2i0000000000-2200000000
χ3222-22-2-22-222-22-22-2-2-222-20000000000002-22-200−2i2i00000000−2i−2i2i2i00000000−2i2i−2i2i00000000002-200000000
χ3322-22-2-22-22-22-222-2-2-222-2000000000000-22-222i−2i0000002i2i−2i−2i0000000000002i−2i−2i2i00000000000002-200000
χ3422-22-2-22-22-22-222-2-2-222-2000000000000-22-222i−2i0000002i2i−2i−2i000000000000−2i2i2i−2i0000000000000-2200000
χ3522-22-2-22-22-22-222-2-2-222-2000000000000-22-22−2i2i000000−2i−2i2i2i0000000000002i−2i−2i2i0000000000000-2200000
χ3622-22-2-22-22-22-222-2-2-222-2000000000000-22-22−2i2i000000−2i−2i2i2i000000000000−2i2i2i−2i00000000000002-200000
χ372-2-2-22-222222-2-2-222-22-2-22-22-222-2-2000022-2-20000002-2000000000000000000002i2i−2i−2i0000000000002i−2i00
χ382-2-2-22-222222-2-2-222-22-2-22-22-222-2-2000022-2-20000002-200000000000000000000−2i−2i2i2i000000000000−2i2i00
χ392-2-2-22-222222-2-2-222-22-2-2-22-22-2-222000022-2-2000000-22000000000000000000002i2i−2i−2i000000000000−2i2i00
χ402-2-2-22-222222-2-2-222-22-2-2-22-22-2-222000022-2-2000000-2200000000000000000000−2i−2i2i2i0000000000002i−2i00
χ412-2-2-22-2222-2-222-222-22-2-22-2-2222-2-222-2-2-2-22200002-2-220000000022-2-222-2-2000000000000000000000000
χ422-2-2-22-2222-2-222-222-22-2-22-2-2222-2-2-2-222-2-2220000-22-2200000000-2-222-2-222000000000000000000000000
χ432-2-2-22-2222-2-222-222-22-2-2-222-2-2-22222-2-2-2-2220000-222-20000000022-2-2-2-222000000000000000000000000
χ442-2-2-22-2222-2-222-222-22-2-2-222-2-2-222-2-222-2-22200002-22-200000000-2-22222-2-2000000000000000000000000
χ452-2-2-22-222-1-2-2221-1-11-1112-2-22-1-11122-2-211-1-100002-21-13−33−33−33−3-1-111-1-11100000000003−33−30000000000
χ462-2-2-22-222-1-2-2221-1-11-1112-2-22-1-11122-2-211-1-100002-21-1−33−33−33−33-1-111-1-1110000000000−33−330000000000
χ472-2-2-22-222-1-2-2221-1-11-1112-2-22-1-111-2-22211-1-10000-221-13−33−33−33−311-1-111-1-10000000000−33−330000000000
χ482-2-2-22-222-1-2-2221-1-11-1112-2-22-1-111-2-22211-1-10000-221-1−33−33−33−3311-1-111-1-100000000003−33−30000000000
χ492-2-2-22-222-1-2-2221-1-11-111-222-211-1-122-2-211-1-10000-22-113−33−3−33−33-1-11111-1-100000000003−3−330000000000
χ502-2-2-22-222-1-2-2221-1-11-111-222-211-1-122-2-211-1-10000-22-11−33−333−33−3-1-11111-1-10000000000−333−30000000000
χ512-2-2-22-222-1-2-2221-1-11-111-222-211-1-1-2-22211-1-100002-2-113−33−3−33−3311-1-1-1-1110000000000−333−30000000000
χ522-2-2-22-222-1-2-2221-1-11-111-222-211-1-1-2-22211-1-100002-2-11−33−333−33−311-1-1-1-11100000000003−3−330000000000
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
χ55444-44-4-4-44000044-44-4-4-40000000022−2222−220000000000000000000022−2222−220000000000000000000000000000
χ56444-44-4-4-44000044-44-4-4-400000000−2222−222200000000000000000000−2222−22220000000000000000000000000000
χ57444-44-4-4-4-20000-2-22-22220000−2i32i3−2i32i322−2222−2200000000000000000000−22−22i6−i6i6−i6000000000000000000000000
χ58444-44-4-4-4-20000-2-22-22220000−2i32i3−2i32i3−2222−2222000000000000000000002−22−2−i6i6−i6i6000000000000000000000000
χ59444-44-4-4-4-20000-2-22-222200002i3−2i32i3−2i322−2222−2200000000000000000000−22−22−i6i6−i6i6000000000000000000000000
χ60444-44-4-4-4-20000-2-22-222200002i3−2i32i3−2i3−2222−2222000000000000000000002−22−2i6−i6i6−i6000000000000000000000000
χ6144-44-4-44-4-24-44-4-2222-2-22000000000000-22-22004i−4i00000000−2i−2i2i2i00000000000000000000000000000000
χ6244-44-4-44-4-24-44-4-2222-2-22000000000000-22-2200−4i4i000000002i2i−2i−2i00000000000000000000000000000000
χ6344-44-4-44-4-2-44-44-2222-2-220000000000002-22-24i−4i000000−2i−2i2i2i000000000000000000000000000000000000
χ6444-44-4-44-4-2-44-44-2222-2-220000000000002-22-2−4i4i0000002i2i−2i−2i000000000000000000000000000000000000
χ6544-4-4-44-44400004-44-4-4-440000000000000000000000000000000000000000000022−2222−220000000000000000
χ6644-4-4-44-44400004-44-4-4-4400000000000000000000000000000000000000000000−2222−22220000000000000000
χ674-444-4-4-4440000-4-444-44-400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ684-444-4-4-4440000-4-444-44-4000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ694-44-4-444-444-4-44-4-4-444-440000000000004-4-44000000000000000000000000000000000000000000000000
χ704-44-4-444-44-444-4-4-4-444-44000000000000-444-4000000000000000000000000000000000000000000000000
χ714-44-4-444-4-24-4-44222-2-22-2000000000000-222-200000000−2i32i32i3−2i3000000000000000000000000000000000000
χ724-44-4-444-4-24-4-44222-2-22-2000000000000-222-2000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ734-44-4-444-4-2-444-4222-2-22-20000000000002-2-22000000000000−2i32i32i3−2i300000000000000000000000000000000
χ744-44-4-444-4-2-444-4222-2-22-20000000000002-2-220000000000002i3−2i3−2i32i300000000000000000000000000000000
χ754-4-4444-4-440000-44-4-4-4440000000022−22−22220000000000000000000022−22−22220000000000000000000000000000
χ764-4-4444-4-440000-44-4-4-44400000000−222222−2200000000000000000000−222222−220000000000000000000000000000
χ774-4-4444-4-4-200002-2222-2-20000−2i32i32i3−2i322−22−222200000000000000000000−222−2i6−i6−i6i6000000000000000000000000
χ784-4-4444-4-4-200002-2222-2-20000−2i32i32i3−2i3−222222−22000000000000000000002−2−22−i6i6i6−i6000000000000000000000000
χ794-4-4444-4-4-200002-2222-2-200002i3−2i3−2i32i322−22−222200000000000000000000−222−2−i6i6i6−i6000000000000000000000000
χ804-4-4444-4-4-200002-2222-2-200002i3−2i3−2i32i3−222222−22000000000000000000002−2−22i6−i6−i6i6000000000000000000000000
χ814-4-4-44-444-244-4-42-2-22-2224-44-4-2-2220000-2-222000000-220000000000000000000000000000000000000000
χ824-4-4-44-444-244-4-42-2-22-222-44-4422-2-20000-2-2220000002-20000000000000000000000000000000000000000
χ8388-8-8-88-88-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000
χ848-888-8-8-88-4000044-4-44-440000000000000000000000000000000000000000000000000000000000000000

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