Finite Group Databasebeta

← Group #10830975

Character table — Group #10830975

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222224444444488888888888888888888121212121212121212121212161616161616161616162424242424244848
order1222222234444666666688881212121222444488121212122424242424242424222244448888446612121212121222228844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111
χ4111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ51111111111111111111111111111-1-111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111111-1-1-1-111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111
χ911111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11-111-1-111-1-111-1-1-1-11-1
χ1011111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-111-1-1-1-11111-11
χ1111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1111-1-1-1-111-1-111111-1
χ1211111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1111-1-1-1-11111-1-1-1-1-11
χ1311111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1-111-1-111-1-1-11
χ1411111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-11111-1-1111-1
χ1511111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11-1-1-11111-1-111-1-111-11
χ1611111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111111-1-1-11111-1-1-1-111-1-11-1
χ17222222222-2-2-2-222222220000-2-2-2-2002-2000022-2-2000000002222-2-2-2-20000000000000000000000
χ18222222222-2-2-2-222222220000-2-2-2-2002-2000022-2-200000000-2-2-2-222220000000000000000000000
χ19222222222-2-2-2-222222220000-2-2-2-200-220000-2-2220000000022-2-2-2-2220000000000000000000000
χ20222222222-2-2-2-222222220000-2-2-2-200-220000-2-22200000000-2-22222-2-20000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1-1-1-1-100000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-122-2-222-2-21111-1-1-1-11111000000000000-2-2-1-1-1-1111100000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-222-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-21111111100000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-11111000000000000221111-1-1-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-12222-2-2-2-2-1-1-1-1111111110000000000002-2-1-111-1-11100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-2-22211111111-1-1-1-1000000000000-22-1-11111-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22222-2-2-1-1-1-111111111000000000000-2211-1-111-1-100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-2-2-2222211111111-1-1-1-10000000000002-211-1-1-1-11100000000
χ2922-2-22-2-2222-2-222-2-2-2-22222-2-22-22-200000000000022-2-2000000000000000000000000002-22-20000
χ3022-2-22-2-2222-2-222-2-2-2-22222-2-22-22-200000000000022-2-200000000000000000000000000-22-220000
χ3122-2-22-2-2222-2-222-2-2-2-222-2-2222-22-2000000000000-2-222000000000000000000000000002-2-220000
χ3222-2-22-2-2222-2-222-2-2-2-222-2-2222-22-2000000000000-2-22200000000000000000000000000-222-20000
χ332-222-2-2-22222-2-2-2-2-2222-2000022-2-20000002i−2i000000002i2i−2i−2i002-2002-22i2i−2i−2i000000000000000000
χ342-222-2-2-22222-2-2-2-2-2222-2000022-2-20000002i−2i000000002i2i−2i−2i00-2200-22−2i−2i2i2i000000000000000000
χ352-222-2-2-22222-2-2-2-2-2222-2000022-2-2000000−2i2i00000000−2i−2i2i2i002-2002-2−2i−2i2i2i000000000000000000
χ362-222-2-2-22222-2-2-2-2-2222-2000022-2-2000000−2i2i00000000−2i−2i2i2i00-2200-222i2i−2i−2i000000000000000000
χ372-222-2-2-222-2-222-2-2-2222-22-22-2-2-2220000000000002-22-20000002-200-220000000000000000002-200
χ382-222-2-2-222-2-222-2-2-2222-22-22-2-2-2220000000000002-22-2000000-22002-2000000000000000000-2200
χ392-222-2-2-222-2-222-2-2-2222-2-22-22-2-222000000000000-22-220000002-200-22000000000000000000-2200
χ402-222-2-2-222-2-222-2-2-2222-2-22-22-2-222000000000000-22-22000000-22002-20000000000000000002-200
χ412-2-2-2-22222-22-22-222-2-22-22-2-22-222-22-2002-20000002-2-220000000000000000002-22-2000000000000
χ422-2-2-2-22222-22-22-222-2-22-22-2-22-222-2-2200-220000002-2-22000000000000000000-22-22000000000000
χ432-2-2-2-22222-22-22-222-2-22-2-222-2-222-22-200-22000000-222-20000000000000000002-2-22000000000000
χ442-2-2-2-22222-22-22-222-2-22-2-222-2-222-2-22002-2000000-222-2000000000000000000-222-2000000000000
χ452-2-2-2-2222-1-22-221-1-111-112-2-221-1-112-2002-2003−33−3-111-13−33−300000000000000-11-113−33−300000000
χ462-2-2-2-2222-1-22-221-1-111-112-2-221-1-112-2002-200−33−33-111-1−33−3300000000000000-11-11−33−3300000000
χ472-2-2-2-2222-1-22-221-1-111-112-2-221-1-11-2200-22003−33−3-111-13−33−3000000000000001-11-1−33−3300000000
χ482-2-2-2-2222-1-22-221-1-111-112-2-221-1-11-2200-2200−33−33-111-1−33−33000000000000001-11-13−33−300000000
χ492-2-2-2-2222-1-22-221-1-111-11-222-21-1-112-200-22003−33−31-1-11−33−3300000000000000-111-13−3−3300000000
χ502-2-2-2-2222-1-22-221-1-111-11-222-21-1-112-200-2200−33−331-1-113−33−300000000000000-111-1−333−300000000
χ512-2-2-2-2222-1-22-221-1-111-11-222-21-1-11-22002-2003−33−31-1-11−33−33000000000000001-1-11−333−300000000
χ522-2-2-2-2222-1-22-221-1-111-11-222-21-1-11-22002-200−33−331-1-113−33−3000000000000001-1-113−3−3300000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200002222004-40000-2-22200000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000222200-44000022-2-200000000000000000000000000000000000000
χ55444-4-44-4-44000044-44-4-4-4000000000000000000000000000000004i−4i000000000000000000000000
χ56444-4-44-4-44000044-44-4-4-400000000000000000000000000000000−4i4i000000000000000000000000
χ5744-44-4-44-4400004-44-44-4-4000000000000000000000000000000000000−2i22i2−2i22i2000000000000000000
χ5844-44-4-44-4400004-44-44-4-40000000000000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ5944-4-44-4-444-444-44-4-4-4-4440000-44-4400000000000000000000000000000000000000000000000000
χ6044-4-44-4-44-24-4-44-22222-2-244-4-4-22-22000000000000-2-2220000000000000000000000000000000000
χ6144-4-44-4-44-24-4-44-22222-2-2-4-444-22-2200000000000022-2-20000000000000000000000000000000000
χ6244-4-44-4-44-2-444-4-22222-2-200002-22-20000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ6344-4-44-4-44-2-444-4-22222-2-200002-22-200000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ644-444-4-4-44-244-4-4222-2-2-220000-2-2220000004i−4i00000000−2i−2i2i2i000000000000000000000000000000
χ654-444-4-4-44-244-4-4222-2-2-220000-2-222000000−4i4i000000002i2i−2i−2i000000000000000000000000000000
χ664-444-4-4-44-2-4-444222-2-2-224-44-422-2-2000000000000-22-220000000000000000000000000000000000
χ674-444-4-4-44-2-4-444222-2-2-22-44-4422-2-20000000000002-22-20000000000000000000000000000000000
χ684-44-44-44-440000-4-444-4-4400000000000000000000000000004-40000000000000000000000000000
χ694-44-44-44-440000-4-444-4-440000000000000000000000000000-440000000000000000000000000000
χ704-4-4444-4-440000-44-4-44-4400000000000000000000000000000000000022−22−2222000000000000000000
χ714-4-4444-4-440000-44-4-44-44000000000000000000000000000000000000−222222−22000000000000000000
χ724-4-4-4-444444-44-4-444-4-44-400004-4-4400000000000000000000000000000000000000000000000000
χ734-4-4-4-4444-24-44-42-2-222-220000-222-20000000023−23−232300000000000000000000000000000000000000
χ744-4-4-4-4444-24-44-42-2-222-220000-222-200000000−232323−2300000000000000000000000000000000000000
χ75888-8-88-8-8-40000-4-44-44440000000000000000000000000000000000000000000000000000000000
χ7688-88-8-88-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000
χ778-88-88-88-8-4000044-4-444-40000000000000000000000000000000000000000000000000000000000
χ788-8-8888-8-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000

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