Finite Group Databasebeta

← Group #10846087

Character table — Group #10846087

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222224444444488888888888888888888121212121212121212121212161616161616161616162424242424244848
order1222222234444666666622441212121244446688881212242424242424242444448888888844121212121212121224444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111-1-1111-1-11-11
χ4111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-111-1-1-1-1-111-11-1
χ51111111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-111-1-1111-1-11111-1
χ61111111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-111-111-1-1-1-11
χ71111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1
χ81111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ911111111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-11111-1-1-1
χ1011111111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111-1-1-1-1111
χ1111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111111-11111-1-1-1-1-111-1-1-11-1
χ1211111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11111-1-1-1-11-1-1111-11
χ1311111111111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-11-1-1-1-11111-1-1-111-1-11
χ1411111111111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-1-1-11111111-1-111-1
χ1511111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111
χ1611111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1111111-1-1
χ17222222222-2-2-2-2222222222-2-2-2-2-2-20000220000-2-20000000022-2-2000000000000000000-20000200
χ18222222222-2-2-2-2222222222-2-2-2-2-2-20000220000-2-200000000-2-22200000000000000000020000-200
χ19222222222-2-2-2-22222222-2-222-2-2-2-20000-2-20000220000000022-2-200000000000000000020000-200
χ20222222222-2-2-2-22222222-2-222-2-2-2-20000-2-200002200000000-2-222000000000000000000-20000200
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1-1-1-1-100000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-122-2-2-1-1-2-2-2-2-1-111111111000000000000-22-1-111-1-11100000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-222-1-1-2-2-2-2-1-1111111110000000000002-211-1-111-1-100000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-1000000000000-2-21111111100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122221122-2-211-1-1-1-11111000000000000-2-2-1-11111-1-100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-211-2-222111111-1-1-1-10000000000002-2-1-1-1-1111100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211-2-222111111-1-1-1-1000000000000-221111-1-1-1-100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-2-2-21122-2-211-1-1-1-111110000000000002211-1-1-1-11100000000
χ29222-2-2-2-2222-22-22-2-2-22-2200002-22-22-200000000000000000000002i2i−2i−2i0000002-20000000002i−2i000
χ30222-2-2-2-2222-22-22-2-2-22-2200002-22-22-20000000000000000000000−2i−2i2i2i0000002-2000000000−2i2i000
χ31222-2-2-2-2222-22-22-2-2-22-2200002-22-2-2200000000000000000000002i2i−2i−2i000000-22000000000−2i2i000
χ32222-2-2-2-2222-22-22-2-2-22-2200002-22-2-220000000000000000000000−2i−2i2i2i000000-220000000002i−2i000
χ332-2-22-2-222222-2-2-222-2-2-22000022-2-20000002i−2i00002i2i−2i−2i00002-22-22i−2i2i−2i0000000000000000000000
χ342-2-22-2-222222-2-2-222-2-2-22000022-2-20000002i−2i00002i2i−2i−2i0000-22-22−2i2i−2i2i0000000000000000000000
χ352-2-22-2-222222-2-2-222-2-2-22000022-2-2000000−2i2i0000−2i−2i2i2i00002-22-2−2i2i−2i2i0000000000000000000000
χ362-2-22-2-222222-2-2-222-2-2-22000022-2-2000000−2i2i0000−2i−2i2i2i0000-22-222i−2i2i−2i0000000000000000000000
χ372-2-22-2-2222-2-222-222-2-2-220000-2-222000000002-200000022-2-22-2-22000022-2-2000000000000000000
χ382-2-22-2-2222-2-222-222-2-2-220000-2-222000000002-200000022-2-2-222-20000-2-222000000000000000000
χ392-2-22-2-2222-2-222-222-2-2-220000-2-22200000000-22000000-2-2222-2-220000-2-222000000000000000000
χ402-2-22-2-2222-2-222-222-2-2-220000-2-22200000000-22000000-2-222-222-2000022-2-2000000000000000000
χ412-2-2-222-2222-2-22-2-2-22-22200002-2-22002-2000000000000000000002-2-220000000000002-202-200000
χ422-2-2-222-2222-2-22-2-2-22-22200002-2-22002-200000000000000000000-222-20000000000002-20-2200000
χ432-2-2-222-2222-2-22-2-2-22-22200002-2-2200-22000000000000000000002-2-22000000000000-220-2200000
χ442-2-2-222-2222-2-22-2-2-22-22200002-2-2200-2200000000000000000000-222-2000000000000-2202-200000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-244-4-422220000-2-200002200000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422220000220000-2-200000000000000000000000000000000000000
χ47444-4-4-4-444-44-444-4-4-44-440000-44-4400000000000000000000000000000000000000000000000000
χ48444-4-4-4-44-24-44-4-2222-22-20000-22-224-400000000000000000000000000000000-2200000000000000
χ49444-4-4-4-44-24-44-4-2222-22-20000-22-22-44000000000000000000000000000000002-200000000000000
χ50444-4-4-4-44-2-44-44-2222-22-200002-22-200000000000000000000000000000000000000−2i32i30000000000
χ51444-4-4-4-44-2-44-44-2222-22-200002-22-2000000000000000000000000000000000000002i3−2i30000000000
χ5244-44-44-4-44000044-4-4-44-400000000000000000000000000000000000022−2222−22000000000000000000
χ5344-44-44-4-44000044-4-4-44-4000000000000000000000000000000000000−2222−2222000000000000000000
χ5444-4-44-44-4400004-444-4-4-44-400000000004-400000000000000000000000000000000000000000000
χ5544-4-44-44-4400004-444-4-4-4-440000000000-4400000000000000000000000000000000000000000000
χ5644-4-44-44-4-20000-22-2-22224-40000000000-22000000i6−i6i6−i6i6−i6i6−i6000000000000000000000000000000
χ5744-4-44-44-4-20000-22-2-22224-40000000000-22000000−i6i6−i6i6−i6i6−i6i6000000000000000000000000000000
χ5844-4-44-44-4-20000-22-2-2222-4400000000002-2000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000000000
χ5944-4-44-44-4-20000-22-2-2222-4400000000002-2000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000000000
χ604-4444-4-4-440000-44-444-4-400000000000000000000000000000000000022−22−2222000000000000000000
χ614-4444-4-4-440000-44-444-4-4000000000000000000000000000000000000−222222−22000000000000000000
χ624-44-4-444-440000-4-44-444-4004i−4i000000000000004i−4i00000000000000000000000000000000000000
χ634-44-4-444-440000-4-44-444-400−4i4i00000000000000−4i4i00000000000000000000000000000000000000
χ644-44-4-444-4-2000022-22-2-22004i−4i00000000000000−2i2i6−6−66i6−i6−i6i6000000000000000000000000000000
χ654-44-4-444-4-2000022-22-2-22004i−4i00000000000000−2i2i−666−6−i6i6i6−i6000000000000000000000000000000
χ664-44-4-444-4-2000022-22-2-2200−4i4i000000000000002i−2i6−6−66−i6i6i6−i6000000000000000000000000000000
χ674-44-4-444-4-2000022-22-2-2200−4i4i000000000000002i−2i−666−6i6−i6−i6i6000000000000000000000000000000
χ684-4-44-4-444-244-4-42-2-2222-20000-2-2220000004i−4i0000−2i−2i2i2i0000000000000000000000000000000000
χ694-4-44-4-444-244-4-42-2-2222-20000-2-222000000−4i4i00002i2i−2i−2i0000000000000000000000000000000000
χ704-4-44-4-444-2-4-4442-2-2222-2000022-2-2000000004-4000000-2-222000000000000000000000000000000
χ714-4-44-4-444-2-4-4442-2-2222-2000022-2-200000000-4400000022-2-2000000000000000000000000000000
χ724-4-4-444-444-444-4-4-4-44-4440000-444-400000000000000000000000000000000000000000000000000
χ734-4-4-444-44-24-4-44222-22-2-20000-222-2004-4000000000000000000000000000000000000-2200000000
χ744-4-4-444-44-24-4-44222-22-2-20000-222-200-440000000000000000000000000000000000002-200000000
χ754-4-4-444-44-2-444-4222-22-2-200002-2-22000000000000000000000000000000000000−2i32i3000000000000
χ764-4-4-444-44-2-444-4222-22-2-200002-2-220000000000000000000000000000000000002i3−2i3000000000000
χ7788-88-88-8-8-40000-4-4444-440000000000000000000000000000000000000000000000000000000000
χ788-8888-8-8-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000

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