Finite Group Databasebeta

← Group #10845377

Character table — Group #10845377

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444446666888888888888888888881212121212121616161616161616161624242424242424244848
order12222222344446666666888812121212444422244466881212242424242424242444888844661212121212122444448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-111-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-11-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ51111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-111-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-11-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1
χ911111111111111111111-1-1-1-111111111111-1-1111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-111-1-111-1-111-1-11-1
χ1011111111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11-111-1-1-1-111-1-1-1-11111-11
χ1111111111111111111111-1-1-1-111111111-1-1111111-1-111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-111-1-1111111-1-1-1-1-11
χ1211111111111111111111-1-1-1-111111111-1-1-111-1-1-111-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-111-1-1111-1
χ1311111111111111111111-1-1-1-11111-1-1-1-1111-1-1111-1-111-1-1-1-1-1-1-1-1-1-11111-1111-1-111-1-1-1-111-1-111-11
χ1411111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111-111-1-1-1-1111111-1-1-1-11-1
χ1511111111111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-111-1-1-1-111111-1
χ1611111111111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-11111-1-11111-11-1-11111-1-111-1-111-1-1-11
χ17222222222-2-2-2-222222220000-2-2-2-2222200200-22200-2-200000000-2-200000000000000-2200000000
χ18222222222-2-2-2-222222220000-2-2-2-2222200-2002-2-2002200000000-2-2000000000000002-200000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-200200-22200-2-20000000022000000000000002-200000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-200-2002-2-20022000000002200000000000000-2200000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-10000222222-1-122-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1000022-222-211-2-211-1-1-1-11111000000-2-2-1-1-1-111110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-10000-2-22-2-22-1-122-1-1-1-1-1-1-1-1-1-1000000-2-2111111110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-10000-2-2-2-2-2-211-2-211-1-1-1-11111000000221111-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000222-2-22-1-1-2-2-1-111111111000000-22-1-111-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1000022-2-2-2-21122111111-1-1-1-10000002-2-1-11111-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-22222-1-1-2-2-1-1111111110000002-211-1-111-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-2-222-21122111111-1-1-1-1000000-2211-1-1-1-1110000000000
χ292222-2-2-2-222-2-222-2-222-2-222-2-22-2-22000000000000000022-2-200000000000000000000002i−2i2i−2i0000
χ302222-2-2-2-222-2-222-2-222-2-222-2-22-2-22000000000000000022-2-20000000000000000000000−2i2i−2i2i0000
χ312222-2-2-2-222-2-222-2-222-2-2-2-2222-2-220000000000000000-2-22200000000000000000000002i−2i−2i2i0000
χ322222-2-2-2-222-2-222-2-222-2-2-2-2222-2-220000000000000000-2-2220000000000000000000000−2i2i2i−2i0000
χ332-2-222-2-22222-2-2-22-22-22-22i−2i2i−2i22-2-222-2-20000000000002i−2i2i−2i00002-22i2i−2i−2i00000000000000000000
χ342-2-222-2-22222-2-2-22-22-22-22i−2i2i−2i22-2-2-2-2220000000000002i−2i2i−2i0000-22−2i−2i2i2i00000000000000000000
χ352-2-222-2-22222-2-2-22-22-22-2−2i2i−2i2i22-2-222-2-2000000000000−2i2i−2i2i00002-2−2i−2i2i2i00000000000000000000
χ362-2-222-2-22222-2-2-22-22-22-2−2i2i−2i2i22-2-2-2-222000000000000−2i2i−2i2i0000-222i2i−2i−2i00000000000000000000
χ372-2-222-2-222-2-222-22-22-22-20000-2-22222-2-2000000002-200000022-2-2-22000000000000000000002-200
χ382-2-222-2-222-2-222-22-22-22-20000-2-22222-2-200000000-22000000-2-222-2200000000000000000000-2200
χ392-2-222-2-222-2-222-22-22-22-20000-2-222-2-222000000002-200000022-2-22-200000000000000000000-2200
χ402-2-222-2-222-2-222-22-22-22-20000-2-222-2-22200000000-22000000-2-2222-2000000000000000000002-200
χ412-2-22-222-222-22-2-2-222-2-222i−2i−2i2i2-22-200002-202i−2i00000002i−2i−2i2i0000000000002-22i−2i00000000000000
χ422-2-22-222-222-22-2-2-222-2-222i−2i−2i2i2-22-20000-220−2i2i00000002i−2i−2i2i000000000000-22−2i2i00000000000000
χ432-2-22-222-222-22-2-2-222-2-22−2i2i2i−2i2-22-200002-20−2i2i0000000−2i2i2i−2i0000000000002-2−2i2i00000000000000
χ442-2-22-222-222-22-2-2-222-2-22−2i2i2i−2i2-22-20000-2202i−2i0000000−2i2i2i−2i000000000000-222i−2i00000000000000
χ452-2-22-222-2-12-22-211-1-111-12i−2i−2i2i-11-1100002-202i−2i0−i3i300−i3i3−iii−i3−33−300000000-11−ii−i3i33−30000000000
χ462-2-22-222-2-12-22-211-1-111-12i−2i−2i2i-11-1100002-202i−2i0i3−i300i3−i3−iii−i−33−3300000000-11−iii3−i3−330000000000
χ472-2-22-222-2-12-22-211-1-111-12i−2i−2i2i-11-110000-220−2i2i0−i3i300−i3i3−iii−i3−33−3000000001-1i−ii3−i3−330000000000
χ482-2-22-222-2-12-22-211-1-111-12i−2i−2i2i-11-110000-220−2i2i0i3−i300i3−i3−iii−i−33−33000000001-1i−i−i3i33−30000000000
χ492-2-22-222-2-12-22-211-1-111-1−2i2i2i−2i-11-1100002-20−2i2i0−i3i300−i3i3i−i−ii−33−3300000000-11i−i−i3i3−330000000000
χ502-2-22-222-2-12-22-211-1-111-1−2i2i2i−2i-11-1100002-20−2i2i0i3−i300i3−i3i−i−ii3−33−300000000-11i−ii3−i33−30000000000
χ512-2-22-222-2-12-22-211-1-111-1−2i2i2i−2i-11-110000-2202i−2i0−i3i300−i3i3i−i−ii−33−33000000001-1−iii3−i33−30000000000
χ522-2-22-222-2-12-22-211-1-111-1−2i2i2i−2i-11-110000-2202i−2i0i3−i300i3−i3i−i−ii3−33−3000000001-1−ii−i3i3−330000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200002222000000400-4-2-200220000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-200002222000000-40042200-2-20000000000000000000000000000000000
χ554444-4-4-4-44-444-44-4-444-4-40000-444-400000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-24-4-44-222-2-22244-4-4-222-20000000000000000-2-222000000000000000000000000000000
χ574444-4-4-4-4-24-4-44-222-2-222-4-444-222-2000000000000000022-2-2000000000000000000000000000000
χ584444-4-4-4-4-2-444-4-222-2-22200002-2-220000000000000000000023−23−232300000000000000000000000000
χ594444-4-4-4-4-2-444-4-222-2-22200002-2-2200000000000000000000−232323−2300000000000000000000000000
χ6044-4-44-44-4400004-4-4-4-444000000004i−4i4i−4i0000000000000000000000000000000000000000000000
χ6144-4-44-44-4400004-4-4-4-44400000000−4i4i−4i4i0000000000000000000000000000000000000000000000
χ6244-4-4-44-4440000444-4-4-4-40000000000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ6344-4-4-44-4440000444-4-4-4-400000000000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ644-44-444-4-440000-4-44-444-4000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ654-44-444-4-440000-4-44-444-400000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ664-44-4-4-44440000-44-4-44-44000000000000000000000000000000000022−22−222200000000000000000000
χ674-44-4-4-44440000-44-4-44-440000000000000000000000000000000000−222222−2200000000000000000000
χ684-4-444-4-44-244-4-42-22-22-224i−4i4i−4i-2-2220000000000000000−2i2i−2i2i000000000000000000000000000000
χ694-4-444-4-44-244-4-42-22-22-22−4i4i−4i4i-2-22200000000000000002i−2i2i−2i000000000000000000000000000000
χ704-4-444-4-44-2-4-4442-22-22-22000022-2-20000000000004-4000000-2-22200000000000000000000000000
χ714-4-444-4-44-2-4-4442-22-22-22000022-2-2000000000000-4400000022-2-200000000000000000000000000
χ724-4-44-444-44-44-44-4-444-4-440000-44-4400000000000000000000000000000000000000000000000000
χ734-4-44-444-4-2-44-4422-2-222-200002-22-20000000000−2i32i3002i3−2i30000000000000000000000000000000000
χ744-4-44-444-4-2-44-4422-2-222-200002-22-200000000002i3−2i300−2i32i30000000000000000000000000000000000
χ7588-8-88-88-8-40000-44444-4-40000000000000000000000000000000000000000000000000000000000
χ7688-8-8-88-88-40000-4-4-444440000000000000000000000000000000000000000000000000000000000
χ778-88-888-8-8-4000044-44-4-440000000000000000000000000000000000000000000000000000000000
χ788-88-8-8-888-400004-444-44-40000000000000000000000000000000000000000000000000000000000

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