Finite Group Databasebeta

← Group #10844918

Character table — Group #10844918

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222224444444488888888888888888888121212121212121212121212161616161616161616162424242424244848
order122222223444466666668888121212124444448812121212242424242424242444444444888844121212121212121222448824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-111-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-111-1-111-1-1-1-1-1-1-1-111
χ4111111111111111111111111111111-111-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-111-1-1111111-1-1
χ51111111111111111111111111111-1-11-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111-1-11-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111111-1-111-1-1111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-1-1-11111
χ911111111111111111111-1-1-1-11111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11-111-1-1-1-111-1-111-1-11-1
χ1011111111111111111111-1-1-1-11111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-11111-1-111-11
χ1111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-111111-1-1-1-111-1-1111-1
χ1211111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1111111-111111-1-1-1-1-1-111-1-1-11
χ1311111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-1-111-1-1-1-1-11
χ1411111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-11111-1-1-1-111111-1
χ1511111111111111111111-1-1-1-11111-1-1-111-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11-1-1-1-1-11111-1-11111-11
χ1611111111111111111111-1-1-1-11111-1-1-111-111-1-1-1-1-1-1-1-11111-1-111-1-11111111-1-1-1-1-1111111-1-1-1-11-1
χ17222222222-2-2-2-222222220000-2-2-2-200200-20022-2-20000000022-2-2-2-2220000000000000000000000
χ18222222222-2-2-2-222222220000-2-2-2-200200-20022-2-200000000-2-22222-2-20000000000000000000000
χ19222222222-2-2-2-222222220000-2-2-2-200-200200-2-222000000002222-2-2-2-20000000000000000000000
χ20222222222-2-2-2-222222220000-2-2-2-200-200200-2-22200000000-2-2-2-222220000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-122-222-2-2-21111-1-1-1-11111000000000000-2-2-1-111-1-11100000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-22-2-2222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-21111111100000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-111110000000000002211-1-111-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1222-2-22-2-2-1-1-1-1111111110000000000002-2-1-11111-1-100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-2-22211111111-1-1-1-1000000000000-22-1-1-1-1111100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22222-2-2-1-1-1-111111111000000000000-2211-1-1-1-11100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-2-222-22211111111-1-1-1-10000000000002-21111-1-1-1-100000000
χ292222-2-2-2-222-2-222-2-22-22-22i2i−2i−2i2-22-20000000000002i2i−2i−2i000000000000000000000000002-22i−2i0000
χ302222-2-2-2-222-2-222-2-22-22-22i2i−2i−2i2-22-20000000000002i2i−2i−2i00000000000000000000000000-22−2i2i0000
χ312222-2-2-2-222-2-222-2-22-22-2−2i−2i2i2i2-22-2000000000000−2i−2i2i2i000000000000000000000000002-2−2i2i0000
χ322222-2-2-2-222-2-222-2-22-22-2−2i−2i2i2i2-22-2000000000000−2i−2i2i2i00000000000000000000000000-222i−2i0000
χ332-2-222-22-222-22-2-22-2-222-22-22-22-2-222i−2i02i−2i00000002-22-20000000000000000002i−2i002i−2i0000000000
χ342-2-222-22-222-22-2-22-2-222-22-22-22-2-22−2i2i0−2i2i00000002-22-2000000000000000000−2i2i00−2i2i0000000000
χ352-2-222-22-222-22-2-22-2-222-2-22-222-2-222i−2i0−2i2i0000000-22-220000000000000000002i−2i00−2i2i0000000000
χ362-2-222-22-222-22-2-22-2-222-2-22-222-2-22−2i2i02i−2i0000000-22-22000000000000000000−2i2i002i−2i0000000000
χ372-2-222-22-2-12-22-21-111-1-112-22-2-111-12i−2i02i−2i0003−33−3-11-1133−3−300000000000000−ii−i3i3−ii−i3i300000000
χ382-2-222-22-2-12-22-21-111-1-112-22-2-111-12i−2i02i−2i000−33−33-11-11−3−33300000000000000−iii3−i3−iii3−i300000000
χ392-2-222-22-2-12-22-21-111-1-112-22-2-111-1−2i2i0−2i2i0003−33−3-11-1133−3−300000000000000i−ii3−i3i−ii3−i300000000
χ402-2-222-22-2-12-22-21-111-1-112-22-2-111-1−2i2i0−2i2i000−33−33-11-11−3−33300000000000000i−i−i3i3i−i−i3i300000000
χ412-2-222-22-2-12-22-21-111-1-11-22-22-111-12i−2i0−2i2i0003−33−31-11-1−3−33300000000000000−iii3−i3i−i−i3i300000000
χ422-2-222-22-2-12-22-21-111-1-11-22-22-111-12i−2i0−2i2i000−33−331-11-133−3−300000000000000−ii−i3i3i−ii3−i300000000
χ432-2-222-22-2-12-22-21-111-1-11-22-22-111-1−2i2i02i−2i0003−33−31-11-1−3−33300000000000000i−i−i3i3−iii3−i300000000
χ442-2-222-22-2-12-22-21-111-1-11-22-22-111-1−2i2i02i−2i000−33−331-11-133−3−300000000000000i−ii3−i3−ii−i3i300000000
χ452-2-22-22-22222-2-2-2-22-2-2222i−2i−2i2i22-2-20000000000002i−2i−2i2i0000002-2002-20000000000000000002i−2i00
χ462-2-22-22-22222-2-2-2-22-2-2222i−2i−2i2i22-2-20000000000002i−2i−2i2i000000-2200-22000000000000000000−2i2i00
χ472-2-22-22-22222-2-2-2-22-2-222−2i2i2i−2i22-2-2000000000000−2i2i2i−2i0000002-2002-2000000000000000000−2i2i00
χ482-2-22-22-22222-2-2-2-22-2-222−2i2i2i−2i22-2-2000000000000−2i2i2i−2i000000-2200-220000000000000000002i−2i00
χ492-2-22-22-222-2-222-2-22-2-2220000-2-2220000002-2000000002-22-2002-200-2222-2-2000000000000000000
χ502-2-22-22-222-2-222-2-22-2-2220000-2-2220000002-2000000002-22-200-22002-2-2-222000000000000000000
χ512-2-22-22-222-2-222-2-22-2-2220000-2-222000000-2200000000-22-22002-200-22-2-222000000000000000000
χ522-2-22-22-222-2-222-2-22-2-2220000-2-222000000-2200000000-22-2200-22002-222-2-2000000000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-20000222200400-400-2-22200000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000222200-40040022-2-200000000000000000000000000000000000000
χ554444-4-4-4-44-444-44-4-44-44-40000-44-4400000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-24-4-44-222-22-224i4i−4i−4i-22-22000000000000−2i−2i2i2i0000000000000000000000000000000000
χ574444-4-4-4-4-24-4-44-222-22-22−4i−4i4i4i-22-220000000000002i2i−2i−2i0000000000000000000000000000000000
χ584444-4-4-4-4-2-444-4-222-22-2200002-22-2000000000000000023−23−2323000000000000000000000000000000
χ594444-4-4-4-4-2-444-4-222-22-2200002-22-20000000000000000−232323−23000000000000000000000000000000
χ6044-4-44-4-444000044-4-4-4-4400000000000000000000000000004i−4i0000000000000000000000000000
χ6144-4-44-4-444000044-4-4-4-440000000000000000000000000000−4i4i0000000000000000000000000000
χ6244-4-4-444-4400004-44-44-4-4000000000000000000000000000000000000−2i22i2−2i22i2000000000000000000
χ6344-4-4-444-4400004-44-44-4-40000000000000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ644-44-444-4-440000-4444-4-4-4000000000000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ654-44-444-4-440000-4444-4-4-40000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ664-44-4-4-44440000-4-4-444-44000000000000000000000000000000004-4000000000000000000000000
χ674-44-4-4-44440000-4-4-444-4400000000000000000000000000000000-44000000000000000000000000
χ684-4-444-44-44-44-44-44-4-444-40000-444-400000000000000000000000000000000000000000000000000
χ694-4-444-44-4-2-44-442-222-2-2200002-2-220000000023−23−232300000000000000000000000000000000000000
χ704-4-444-44-4-2-44-442-222-2-2200002-2-2200000000−232323−2300000000000000000000000000000000000000
χ714-4-44-44-44-244-4-422-222-2-24i−4i−4i4i-2-222000000000000−2i2i2i−2i0000000000000000000000000000000000
χ724-4-44-44-44-244-4-422-222-2-2−4i4i4i−4i-2-2220000000000002i−2i−2i2i0000000000000000000000000000000000
χ734-4-44-44-44-2-4-44422-222-2-2000022-2-20000004-400000000-22-22000000000000000000000000000000
χ744-4-44-44-44-2-4-44422-222-2-2000022-2-2000000-44000000002-22-2000000000000000000000000000000
χ7588-8-88-8-88-40000-4-44444-40000000000000000000000000000000000000000000000000000000000
χ7688-8-8-888-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000
χ778-88-888-8-8-400004-4-4-44440000000000000000000000000000000000000000000000000000000000
χ788-88-8-8-888-40000444-4-44-40000000000000000000000000000000000000000000000000000000000

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