Finite Group Databasebeta

← Group #10844631

Character table — Group #10844631

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order1222222234444666666644121212124444444888812121212242424242424242444444444442661212121212122244488882
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-111-1-111-1-1111-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-111111
χ511111111111111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111-1-1111-1-1-1-1-1-11
χ611111111111111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-111-1-1-1-1-1111111-1
χ711111111111111111111111111-1-11-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-11111-1
χ811111111111111111111111111-1-11-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11
χ911111111111111111111-1-1111111-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-11111-1-111-111-1-111-1
χ1011111111111111111111-1-1111111-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-11-1-111-1-11
χ1111111111111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111111-1-1-1-1-1-1-11111-1-11
χ1211111111111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-111111-1-1-1-1111-1-1-1-111-1
χ1311111111111111111111-1-11111-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1111111-1-1-111-1-1-1
χ1411111111111111111111-1-11111-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1111
χ1511111111111111111111-1-11111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1111111111-1-1-1-111-1-1-1-1-1-1-1111
χ1611111111111111111111-1-11111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1
χ17222222222-2-2-2-2222222222-2-2-2-200-20000000022-2-20000000022220000-2-200000000000-20000000
χ18222222222-2-2-2-2222222222-2-2-2-200-20000000022-2-200000000-2-2-2-20000220000000000020000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-200200000000-2-2220000000022-2-20000-2-20000000000020000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-200200000000-2-22200000000-2-22200002200000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-122222-2-2-2-2-2-2-1-1-1-1111111110000000000-211-1-111-1-10000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-22-2-222-2-2-2-2-1-1-1-11111111100000000002-1-111-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-22-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2111111110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-22222-2-21111-1-1-1-111110000000000-211-1-1-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-2-2-2-2-22211111111-1-1-1-100000000002-1-1-1-111110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-22222-2-22211111111-1-1-1-10000000000-21111-1-1-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222-2-222-2-21111-1-1-1-1111100000000002-1-11111-1-10000000000
χ29222-2-22-2-222-2-22222-2-2-2-2002-2-22000002i−2i0000000000000000000022-2-200000002i−2i00000002i−2i000
χ30222-2-22-2-222-2-22222-2-2-2-2002-2-22000002i−2i00000000000000000000-2-22200000002i−2i0000000−2i2i000
χ31222-2-22-2-222-2-22222-2-2-2-2002-2-2200000−2i2i0000000000000000000022-2-20000000−2i2i0000000−2i2i000
χ32222-2-22-2-222-2-22222-2-2-2-2002-2-2200000−2i2i00000000000000000000-2-2220000000−2i2i00000002i−2i000
χ332-222-2-22-222-22-2-2-222-2-220022-2-20000000002i−2i000000002i2i−2i−2i00002i−2i2i−2i000000000002-200000000
χ342-222-2-22-222-22-2-2-222-2-220022-2-20000000002i−2i000000002i2i−2i−2i0000−2i2i−2i2i00000000000-2200000000
χ352-222-2-22-222-22-2-2-222-2-220022-2-2000000000−2i2i00000000−2i−2i2i2i00002i−2i2i−2i00000000000-2200000000
χ362-222-2-22-222-22-2-2-222-2-220022-2-2000000000−2i2i00000000−2i−2i2i2i0000−2i2i−2i2i000000000002-200000000
χ372-22-22-2-22222-2-2-2-22-222-2002-22-20002i−2i0000000000000000002-2002i−2i−2i2i2-200000002i−2i0000000000
χ382-22-22-2-22222-2-2-2-22-222-2002-22-20002i−2i000000000000000000-2200−2i2i2i−2i-2200000002i−2i0000000000
χ392-22-22-2-22222-2-2-2-22-222-2002-22-2000−2i2i0000000000000000002-200−2i2i2i−2i2-20000000−2i2i0000000000
χ402-22-22-2-22222-2-2-2-22-222-2002-22-2000−2i2i000000000000000000-22002i−2i−2i2i-220000000−2i2i0000000000
χ412-22-22-2-222-2-222-2-22-222-200-22-222-20000000000000000000002-2000000-220002-200000002-200000
χ422-22-22-2-222-2-222-2-22-222-200-22-222-2000000000000000000000-220000002-20002-20000000-2200000
χ432-22-22-2-222-2-222-2-22-222-200-22-22-220000000000000000000002-2000000-22000-220000000-2200000
χ442-22-22-2-222-2-222-2-22-222-200-22-22-22000000000000000000000-220000002-2000-2200000002-200000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-244222200-400000000-2-2220000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-422220040000000022-2-20000000000000000000000000000000000000
χ47444-4-44-4-44-444-4444-4-4-4-400-444-40000000000000000000000000000000000000000000000000000
χ48444-4-44-4-4-24-4-44-2-2-2222200-222-2000004i−4i0000000000000000000000000000000−2i2i000000000000
χ49444-4-44-4-4-24-4-44-2-2-2222200-222-200000−4i4i00000000000000000000000000000002i−2i000000000000
χ50444-4-44-4-4-2-444-4-2-2-22222002-2-220000000000000000000000000000000000−2i32i30000000000000000
χ51444-4-44-4-4-2-444-4-2-2-22222002-2-2200000000000000000000000000000000002i3−2i30000000000000000
χ5244-444-4-4-4400004-4-444-4-40000000000000−2i22i2000000−2i2−2i22i22i2000000000000000000000000000000000
χ5344-444-4-4-4400004-4-444-4-400000000000002i2−2i20000002i22i2−2i2−2i2000000000000000000000000000000000
χ5444-444-4-4-4-20000-222-2-2220000000000000−2i22i2000023−23i2i2−i2−i2i6−i6i6−i600000000000000000000000000000
χ5544-444-4-4-4-20000-222-2-2220000000000000−2i22i20000−2323i2i2−i2−i2−i6i6−i6i600000000000000000000000000000
χ5644-444-4-4-4-20000-222-2-22200000000000002i2−2i2000023−23−i2−i2i2i2−i6i6−i6i600000000000000000000000000000
χ5744-444-4-4-4-20000-222-2-22200000000000002i2−2i20000−2323−i2−i2i2i2i6−i6i6−i600000000000000000000000000000
χ5844-4-4-4-444400004-4-4-4-44400000000000000000000000000000004-40000000000000000000000000
χ5944-4-4-4-444400004-4-4-4-4440000000000000000000000000000000-440000000000000000000000000
χ604-444-4-44-44-44-44-4-444-4-4400-4-4440000000000000000000000000000000000000000000000000000
χ614-444-4-44-4-24-44-422-2-222-200-2-2220000000004i−4i00000000−2i−2i2i2i00000000000000000000000000000
χ624-444-4-44-4-24-44-422-2-222-200-2-222000000000−4i4i000000002i2i−2i−2i00000000000000000000000000000
χ634-444-4-44-4-2-44-4422-2-222-20022-2-2000000000000000−2i32i3−2i32i3000000000000000000000000000000000
χ644-444-4-44-4-2-44-4422-2-222-20022-2-20000000000000002i3−2i32i3−2i3000000000000000000000000000000000
χ654-44-44-4-44-244-4-422-22-2-2200-22-220004i−4i00000000000000000000000000000000000−2i2i0000000000
χ664-44-44-4-44-244-4-422-22-2-2200-22-22000−4i4i000000000000000000000000000000000002i−2i0000000000
χ674-44-44-4-44-2-4-44422-22-2-22002-22-24-40000000000000000000000000000000000-2200000000000000
χ684-44-44-4-44-2-4-44422-22-2-22002-22-2-4400000000000000000000000000000000002-200000000000000
χ694-4-44-44-4440000-44-44-44-44-40000000000000004-4000000000000000000000000000000000000000
χ704-4-44-44-4440000-44-44-44-4-44000000000000000-44000000000000000000000000000000000000000
χ714-4-44-44-44-200002-22-22-224-4000000000000000-22006−6−666−6−6600000000000000000000000000000
χ724-4-44-44-44-200002-22-22-224-4000000000000000-2200−666−6−666−600000000000000000000000000000
χ734-4-44-44-44-200002-22-22-22-440000000000000002-2006−6−66−666−600000000000000000000000000000
χ744-4-44-44-44-200002-22-22-22-440000000000000002-200−666−66−6−6600000000000000000000000000000
χ754-4-4-4444-440000-44-4-44-44000000000000000000000000000000000000000000000000000000022−220
χ764-4-4-4444-440000-44-4-44-440000000000000000000000000000000000000000000000000000000−22220
χ7788-8-8-8-888-40000-44444-4-40000000000000000000000000000000000000000000000000000000000
χ788-8-8-8888-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000

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