Finite Group Databasebeta

← Group #10834027

Character table — Group #10834027

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222224444444488888888888888888888121212121212121212121212161616161616161616162424242424244848
order1222222234444666666688881212121222444488121212122424242424242424224444448888446612121212121222448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11-111-1-1-1-11111-1-111-11
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111111-111-1-1-1-111-1-111-1-11-1
χ51111111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-11-1-11111-1-1-1-111111-1
χ61111111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-11-1-11111-1-111-1-1-1-1-11
χ71111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ81111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ911111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ1111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1111-1-111-1-111-1-1-1-11-1
χ1211111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1111-1-111-1-1-1-11111-11
χ1311111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111111-1-1-111-1-111-1-111-1-1-11
χ1411111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11-1-1-111-1-11111-1-1111-1
χ1511111111111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111
χ1611111111111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1
χ17222222222-2-2-2-222222220000-2-2-2-200002-20022-2-20000000022-2-222-2-20000000000000000000000
χ18222222222-2-2-2-222222220000-2-2-2-200002-20022-2-200000000-2-222-2-2220000000000000000000000
χ19222222222-2-2-2-222222220000-2-2-2-20000-2200-2-222000000002222-2-2-2-20000000000000000000000
χ20222222222-2-2-2-222222220000-2-2-2-20000-2200-2-22200000000-2-2-2-222220000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-122-2-2-2-2-2-21111-1-1-1-111110000000000002-2-1-11111-1-100000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-222-2-2-2-21111-1-1-1-11111000000000000-2211-1-1-1-11100000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-21111111100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1222222-2-2-1-1-1-111111111000000000000-2-2-1-1-1-1111100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-2-22211111111-1-1-1-1000000000000-22-1-111-1-11100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-222-2-22211111111-1-1-1-10000000000002-211-1-111-1-100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-2-2-222-2-2-1-1-1-111111111000000000000221111-1-1-1-100000000
χ2922-2-22-2-2222-22-2222-2-2-2-200002-2-22002i−2i0000000000000000002i−2i2i−2i00000000002i−2i00002-2000000
χ3022-2-22-2-2222-22-2222-2-2-2-200002-2-22002i−2i000000000000000000−2i2i−2i2i00000000002i−2i0000-22000000
χ3122-2-22-2-2222-22-2222-2-2-2-200002-2-2200−2i2i0000000000000000002i−2i2i−2i0000000000−2i2i0000-22000000
χ3222-2-22-2-2222-22-2222-2-2-2-200002-2-2200−2i2i000000000000000000−2i2i−2i2i0000000000−2i2i00002-2000000
χ3322-2-22-2-222-22-22222-2-2-2-20000-222-22-2000000000000000000002i−2i−2i2i000000002-2000000002i−2i0000
χ3422-2-22-2-222-22-22222-2-2-2-20000-222-22-200000000000000000000−2i2i2i−2i000000002-200000000−2i2i0000
χ3522-2-22-2-222-22-22222-2-2-2-20000-222-2-22000000000000000000002i−2i−2i2i00000000-2200000000−2i2i0000
χ3622-2-22-2-222-22-22222-2-2-2-20000-222-2-2200000000000000000000−2i2i2i−2i00000000-22000000002i−2i0000
χ372-2-22-22-22222-2-2-2-222-2-22000022-2-20000002i−2i000000002i2i−2i−2i2-200002-22i2i−2i−2i000000000000000000
χ382-2-22-22-22222-2-2-2-222-2-22000022-2-20000002i−2i000000002i2i−2i−2i-220000-22−2i−2i2i2i000000000000000000
χ392-2-22-22-22222-2-2-2-222-2-22000022-2-2000000−2i2i00000000−2i−2i2i2i2-200002-2−2i−2i2i2i000000000000000000
χ402-2-22-22-22222-2-2-2-222-2-22000022-2-2000000−2i2i00000000−2i−2i2i2i-220000-222i2i−2i−2i000000000000000000
χ412-2-22-22-222-2-222-2-222-2-2222-2-2-2-22200000000000022-2-200002-20000-220000000000000000002-200
χ422-2-22-22-222-2-222-2-222-2-2222-2-2-2-22200000000000022-2-20000-2200002-2000000000000000000-2200
χ432-2-22-22-222-2-222-2-222-2-22-2-222-2-222000000000000-2-22200002-20000-22000000000000000000-2200
χ442-2-22-22-222-2-222-2-222-2-22-2-222-2-222000000000000-2-2220000-2200002-20000000000000000002-200
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-20000222200004-400-2-22200000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2000022220000-440022-2-200000000000000000000000000000000000000
χ47444-4-44-4-4400004-4-4-44-44000000000000000000000000000000000000−2i22i2−2i22i2000000000000000000
χ48444-4-44-4-4400004-4-4-44-440000000000000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ4944-44-4-44-4400004-4-44-44-4−2i22i2−2i22i20000000000000000−2i22i2−2i22i20000000000000000000000000000000000
χ5044-44-4-44-4400004-4-44-44-42i2−2i22i2−2i200000000000000002i2−2i22i2−2i20000000000000000000000000000000000
χ5144-44-4-44-4-20000-222-22-22−2i22i2−2i22i20000000000000023−23i2−i2i2−i2i6−i6i6−i6000000000000000000000000000000
χ5244-44-4-44-4-20000-222-22-22−2i22i2−2i22i200000000000000−2323i2−i2i2−i2−i6i6−i6i6000000000000000000000000000000
χ5344-44-4-44-4-20000-222-22-222i2−2i22i2−2i20000000000000023−23−i2i2−i2i2−i6i6−i6i6000000000000000000000000000000
χ5444-44-4-44-4-20000-222-22-222i2−2i22i2−2i200000000000000−2323−i2i2−i2i2i6−i6i6−i6000000000000000000000000000000
χ5544-4-44-4-44-24-44-4-2-2-222220000-222-2004i−4i00000000000000000000000000000000−2i2i000000000000
χ5644-4-44-4-44-24-44-4-2-2-222220000-222-200−4i4i000000000000000000000000000000002i−2i000000000000
χ5744-4-44-4-44-2-44-44-2-2-2222200002-2-224-400000000000000000000000000000000-2200000000000000
χ5844-4-44-4-44-2-44-44-2-2-2222200002-2-22-44000000000000000000000000000000002-200000000000000
χ594-4444-4-4-440000-44-444-4-4−2i22i22i2−2i20000000000000000−2i22i22i2−2i20000000000000000000000000000000000
χ604-4444-4-4-440000-44-444-4-42i2−2i2−2i22i200000000000000002i2−2i2−2i22i20000000000000000000000000000000000
χ614-4444-4-4-4-200002-22-2-222−2i22i22i2−2i2000000000000−2i32i300i2−i2−i2i26−6−66000000000000000000000000000000
χ624-4444-4-4-4-200002-22-2-222−2i22i22i2−2i20000000000002i3−2i300i2−i2−i2i2−666−6000000000000000000000000000000
χ634-4444-4-4-4-200002-22-2-2222i2−2i2−2i22i2000000000000−2i32i300−i2i2i2−i2−666−6000000000000000000000000000000
χ644-4444-4-4-4-200002-22-2-2222i2−2i2−2i22i20000000000002i3−2i300−i2i2i2−i26−6−66000000000000000000000000000000
χ654-44-4-4-44444-4-44-4-44-444-400004-44-400000000000000000000000000000000000000000000000000
χ664-44-4-4-4444-444-4-4-44-444-40000-44-4400000000000000000000000000000000000000000000000000
χ674-44-4-4-444-24-4-4422-22-2-220000-22-22000000000000000000000000000000000000000023−2300000000
χ684-44-4-4-444-24-4-4422-22-2-220000-22-220000000000000000000000000000000000000000−232300000000
χ694-44-4-4-444-2-444-422-22-2-2200002-22-200000000000000000000000000000000000000−2i32i30000000000
χ704-44-4-4-444-2-444-422-22-2-2200002-22-2000000000000000000000000000000000000002i3−2i30000000000
χ714-4-44-44-44-244-4-422-2-222-20000-2-2220000004i−4i00000000−2i−2i2i2i000000000000000000000000000000
χ724-4-44-44-44-244-4-422-2-222-20000-2-222000000−4i4i000000002i2i−2i−2i000000000000000000000000000000
χ734-4-44-44-44-2-4-44422-2-222-244-4-422-2-2000000000000-2-2220000000000000000000000000000000000
χ744-4-44-44-44-2-4-44422-2-222-2-4-44422-2-200000000000022-2-20000000000000000000000000000000000
χ754-4-4-4444-440000-44-4-4-44400000000000000000000000000000000000022−22−2222000000000000000000
χ764-4-4-4444-440000-44-4-4-444000000000000000000000000000000000000−222222−22000000000000000000
χ77888-8-88-8-8-40000-4444-44-40000000000000000000000000000000000000000000000000000000000
χ788-8-8-8888-8-400004-4444-4-40000000000000000000000000000000000000000000000000000000000

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