Finite Group Databasebeta

← Group #10845256

Character table — Group #10845256

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order1222222234444666666644121212122244444888812121212242424242424242444444444444661212121212122244488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111111111-11111-1-1-1-1-1-1111-1-1-1-1-1
χ4111111111111111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-111111
χ511111111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-11
χ611111111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-11111-1-1-1111111-1
χ711111111111111111111111111-1-1-1-1-1-1111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-11111-1
χ811111111111111111111111111-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11
χ911111111111111111111-1-1111111-1-111-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-111-1-111-1-111-11111-1-1-1
χ1011111111111111111111-1-1111111-1-111-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-111-1-111-1-1-1-11-1-1-1-1111
χ1111111111111111111111-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-111-1-1-111-1-1111
χ1211111111111111111111-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1111-1-1-1-111111-1-111-1-1-1
χ1311111111111111111111-1-11111-1-11111-111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-11111-1-111-1-1-1-1-111-1
χ1411111111111111111111-1-11111-1-11111-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11
χ1511111111111111111111-1-11111-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111111-1-111-1-111-1-1-1-1-111-1-11
χ1611111111111111111111-1-11111-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11-1-111-1-11111111-1-111-1
χ17222222222-2-2-2-2222222222-2-2-2-2000000-2000022-2-20000000022-2-20000-2-20000000000020000000
χ18222222222-2-2-2-2222222222-2-2-2-2000000-2000022-2-200000000-2-22200002200000000000-20000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-200000020000-2-2220000000022220000-2-200000000000-20000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-200000020000-2-22200000000-2-2-2-20000220000000000020000000
χ2122222222-12222-1-1-1-1-1-1-122-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-100000000002-1-1-1-1-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-12222-2-22-2-2-2-2-1-1-1-1111111110000000000-2-1-1-1-111110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-111111111000000000021111-1-1-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-222222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2111111110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-222-2-2-2221111-1-1-1-111110000000000-2-1-111-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-2-2-222-2-211111111-1-1-1-100000000002-1-11111-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-22222-222-2-211111111-1-1-1-10000000000-211-1-1-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-222-2-2-2-2-2221111-1-1-1-111110000000000211-1-111-1-10000000000
χ29222-2-22-2-222-2-2222-2-22-2-2002-22-200000002i−2i00000000002i2i−2i−2i00002i2i−2i−2i000000000002-200000000
χ30222-2-22-2-222-2-2222-2-22-2-2002-22-200000002i−2i00000000002i2i−2i−2i0000−2i−2i2i2i00000000000-2200000000
χ31222-2-22-2-222-2-2222-2-22-2-2002-22-20000000−2i2i0000000000−2i−2i2i2i00002i2i−2i−2i00000000000-2200000000
χ32222-2-22-2-222-2-2222-2-22-2-2002-22-20000000−2i2i0000000000−2i−2i2i2i0000−2i−2i2i2i000000000002-200000000
χ332-2-22-222-222-22-2-2222-2-2-2002-2-2200002i−2i0000000000000000000002-22-200000002i−2i0000000002i−2i0
χ342-2-22-222-222-22-2-2222-2-2-2002-2-2200002i−2i000000000000000000000-22-2200000002i−2i000000000−2i2i0
χ352-2-22-222-222-22-2-2222-2-2-2002-2-220000−2i2i0000000000000000000002-22-20000000−2i2i000000000−2i2i0
χ362-2-22-222-222-22-2-2222-2-2-2002-2-220000−2i2i000000000000000000000-22-220000000−2i2i0000000002i−2i0
χ372-2-2-222-22222-2-2-22-2-2-2220022-2-2002i−2i00000000000000000002-2002i−2i−2i2i2-20002i−2i00000000000000
χ382-2-2-222-22222-2-2-22-2-2-2220022-2-2002i−2i0000000000000000000-2200−2i2i2i−2i-220002i−2i00000000000000
χ392-2-2-222-22222-2-2-22-2-2-2220022-2-200−2i2i00000000000000000002-200−2i2i2i−2i2-2000−2i2i00000000000000
χ402-2-2-222-22222-2-2-22-2-2-2220022-2-200−2i2i0000000000000000000-22002i−2i−2i2i-22000−2i2i00000000000000
χ412-2-2-222-222-2-222-22-2-2-22200-2-2222-20000000000000000000002-2000000-2202-20000000002-200000
χ422-2-2-222-222-2-222-22-2-2-22200-2-2222-2000000000000000000000-220000002-202-2000000000-2200000
χ432-2-2-222-222-2-222-22-2-2-22200-2-222-220000000000000000000002-2000000-220-22000000000-2200000
χ442-2-2-222-222-2-222-22-2-2-22200-2-222-22000000000000000000000-220000002-20-220000000002-200000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-2442222000000-40000-2-2220000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-422220000004000022-2-20000000000000000000000000000000000000
χ47444-4-44-4-44-444-444-4-44-4-400-44-440000000000000000000000000000000000000000000000000000
χ48444-4-44-4-4-24-4-44-2-222-22200-22-2200000004i−4i0000000000−2i−2i2i2i00000000000000000000000000000
χ49444-4-44-4-4-24-4-44-2-222-22200-22-220000000−4i4i00000000002i2i−2i−2i00000000000000000000000000000
χ50444-4-44-4-4-2-444-4-2-222-222002-22-20000000000000002323−23−23000000000000000000000000000000000
χ51444-4-44-4-4-2-444-4-2-222-222002-22-2000000000000000−23−232323000000000000000000000000000000000
χ5244-44-4-4-44400004-44-4-44-4000000000000000−2i22i20000−2i22i2−2i22i2000000000000000000000000000000000
χ5344-44-4-4-44400004-44-4-44-40000000000000002i2−2i200002i2−2i22i2−2i2000000000000000000000000000000000
χ5444-44-4-4-44-20000-22-222-22000000000000000−2i22i20023−23i2−i2i2−i2i6−i6i6−i600000000000000000000000000000
χ5544-44-4-4-44-20000-22-222-22000000000000000−2i22i200−2323i2−i2i2−i2−i6i6−i6i600000000000000000000000000000
χ5644-44-4-4-44-20000-22-222-220000000000000002i2−2i20023−23−i2i2−i2i2−i6i6−i6i600000000000000000000000000000
χ5744-44-4-4-44-20000-22-222-220000000000000002i2−2i200−2323−i2i2−i2i2i6−i6i6−i600000000000000000000000000000
χ5844-4-44-44-4400004-4-44-4-444i−4i0000000000000004i−4i000000000000000000000000000000000000000
χ5944-4-44-44-4400004-4-44-4-44−4i4i000000000000000−4i4i000000000000000000000000000000000000000
χ6044-4-44-44-4-20000-222-222-24i−4i000000000000000−2i2i00i6−i6−i6i66−6−6600000000000000000000000000000
χ6144-4-44-44-4-20000-222-222-24i−4i000000000000000−2i2i00−i6i6i6−i6−666−600000000000000000000000000000
χ6244-4-44-44-4-20000-222-222-2−4i4i0000000000000002i−2i00i6−i6−i6i6−666−600000000000000000000000000000
χ6344-4-44-44-4-20000-222-222-2−4i4i0000000000000002i−2i00−i6i6i6−i66−6−6600000000000000000000000000000
χ644-4444-4-4-440000-4-44-44-4400000000000000000000000000000004i−4i0000000000000000000000000
χ654-4444-4-4-440000-4-44-44-440000000000000000000000000000000−4i4i0000000000000000000000000
χ664-44-4-4-44440000-4-4-4444-40000000000000000000000000000000000000000000000000000022−22000
χ674-44-4-4-44440000-4-4-4444-400000000000000000000000000000000000000000000000000000−2222000
χ684-4-44-444-44-44-44-4444-4-4-400-444-40000000000000000000000000000000000000000000000000000
χ694-4-44-444-4-24-44-42-2-2-222200-222-200004i−4i00000000000000000000000000000000−2i2i000000000000
χ704-4-44-444-4-24-44-42-2-2-222200-222-20000−4i4i000000000000000000000000000000002i−2i000000000000
χ714-4-44-444-4-2-44-442-2-2-2222002-2-22000000000000000000000000000000000000000023−230000000000
χ724-4-44-444-4-2-44-442-2-2-2222002-2-220000000000000000000000000000000000000000−23230000000000
χ734-4-4-444-44-244-4-42-2222-2-200-2-222004i−4i00000000000000000000000000000000−2i2i00000000000000
χ744-4-4-444-44-244-4-42-2222-2-200-2-22200−4i4i000000000000000000000000000000002i−2i00000000000000
χ754-4-4-444-44-2-4-4442-2222-2-20022-2-24-400000000000000000000000000000000-220000000000000000
χ764-4-4-444-44-2-4-4442-2222-2-20022-2-2-44000000000000000000000000000000002-20000000000000000
χ778-8888-8-8-8-4000044-44-44-40000000000000000000000000000000000000000000000000000000000
χ788-88-8-8-888-40000444-4-4-440000000000000000000000000000000000000000000000000000000000

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