Finite Group Databasebeta

← Group #10844921

Character table — Group #10844921

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222224444444488888888888888888888121212121212121212121212161616161616161616162424242424244848
order1222222234444666666688881212121244444488121212122424242424242424444444448888246612121212121244448824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-11-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111-1-11-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111-111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-11-1-11111-1-1-1-111-1-11-1
χ61111111111111111111111111111-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-11-1-11111-1-111-1-111-11
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111111-111-1-1-1-11111-1-1-1-1-11
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11-111-1-1-1-111-1-111111-1
χ911111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11-11111-1-1-1-111-1-1-1-11-1
χ1011111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-1-1-11111-11
χ1111111111111111111111-1-1-1-111111-1-1111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1-1-11111-1-111-1-1-11
χ1211111111111111111111-1-1-1-111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1111111-1-1111-1
χ1311111111111111111111-1-1-1-11111-111-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ1411111111111111111111-1-1-1-11111-111-11111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-1
χ1511111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-111-1-1111111-1-1
χ1611111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111111111-1-111-1-1-1-1-1-1-1-111
χ17222222222-2-2-2-222222220000-2-2-2-2200-2000022-2-20000000022-2-2-2-2220000000000000000000000
χ18222222222-2-2-2-222222220000-2-2-2-2200-2000022-2-200000000-2-22222-2-20000000000000000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-20020000-2-222000000002222-2-2-2-20000000000000000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-20020000-2-22200000000-2-2-2-222220000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-12-2-22-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-222-2-2-2-2-21111-1-1-1-11111000000000000-2211-1-1-1-11100000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-222-2-21111-1-1-1-111110000000000002-2-1-11111-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-12222-2-2-2-2-1-1-1-1111111110000000000002-2-1-1-1-1111100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-12-2-2222-2-2-1-1-1-111111111000000000000-221111-1-1-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-222-2222211111111-1-1-1-1000000000000-2-211-1-111-1-100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-2-2-2-2-22211111111-1-1-1-100000000000022-1-111-1-11100000000
χ2922-222-2-2-222-2-22222-2-2-2-200002-2-2202i−2i00000000000000000000000002i2i−2i−2i00002i−2i0000002-20000
χ3022-222-2-2-222-2-22222-2-2-2-200002-2-2202i−2i0000000000000000000000000−2i−2i2i2i00002i−2i000000-220000
χ3122-222-2-2-222-2-22222-2-2-2-200002-2-220−2i2i00000000000000000000000002i2i−2i−2i0000−2i2i000000-220000
χ3222-222-2-2-222-2-22222-2-2-2-200002-2-220−2i2i0000000000000000000000000−2i−2i2i2i0000−2i2i0000002-20000
χ332-22-22-22-222-22-2-2-22-222-2000022-2-200002i−2i00000000000000000000002-22-2000000002i−2i2i−2i000000
χ342-22-22-22-222-22-2-2-22-222-2000022-2-200002i−2i0000000000000000000000-22-22000000002i−2i−2i2i000000
χ352-22-22-22-222-22-2-2-22-222-2000022-2-20000−2i2i00000000000000000000002-22-200000000−2i2i−2i2i000000
χ362-22-22-22-222-22-2-2-22-222-2000022-2-20000−2i2i0000000000000000000000-22-2200000000−2i2i2i−2i000000
χ372-2-2-222-22222-2-2-2-222-2-2200002-22-20000002i−2i000000002i2i−2i−2i002-2002-22i−2i−2i2i000000000000000000
χ382-2-2-222-22222-2-2-2-222-2-2200002-22-20000002i−2i000000002i2i−2i−2i00-2200-22−2i2i2i−2i000000000000000000
χ392-2-2-222-22222-2-2-2-222-2-2200002-22-2000000−2i2i00000000−2i−2i2i2i002-2002-2−2i2i2i−2i000000000000000000
χ402-2-2-222-22222-2-2-2-222-2-2200002-22-2000000−2i2i00000000−2i−2i2i2i00-2200-222i−2i−2i2i000000000000000000
χ412-2-2-222-222-2-222-2-222-2-2222-2-2-22-2200000000000022-2-20000002-200-220000000000000000002-200
χ422-2-2-222-222-2-222-2-222-2-2222-2-2-22-2200000000000022-2-2000000-22002-2000000000000000000-2200
χ432-2-2-222-222-2-222-2-222-2-22-2-222-22-22000000000000-2-2220000002-200-22000000000000000000-2200
χ442-2-2-222-222-2-222-2-222-2-22-2-222-22-22000000000000-2-222000000-22002-20000000000000000002-200
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-200002222400-40000-2-22200000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-200002222-4004000022-2-200000000000000000000000000000000000000
χ47444-4-4-4-44400004-4-4-44-4400000000000000000000000000004i−4i0000000000000000000000000000
χ48444-4-4-4-44400004-4-4-44-440000000000000000000000000000−4i4i0000000000000000000000000000
χ4944-444-4-4-44-444-4444-4-4-4-40000-444-400000000000000000000000000000000000000000000000000
χ5044-444-4-4-4-24-4-44-2-2-222220000-222-204i−4i000000000000000000000000000000000−2i2i000000000000
χ5144-444-4-4-4-24-4-44-2-2-222220000-222-20−4i4i0000000000000000000000000000000002i−2i000000000000
χ5244-444-4-4-4-2-444-4-2-2-2222200002-2-220000000000000000000000000000000000−2i32i300000000000000
χ5344-444-4-4-4-2-444-4-2-2-2222200002-2-2200000000000000000000000000000000002i3−2i300000000000000
χ5444-4-4-444-4400004-4-44-44-4−2i22i2−2i22i20000000000000000−2i22i2−2i22i20000000000000000000000000000000000
χ5544-4-4-444-4400004-4-44-44-42i2−2i22i2−2i200000000000000002i2−2i22i2−2i20000000000000000000000000000000000
χ5644-4-4-444-4-20000-222-22-22−2i22i2−2i22i2000000000000−2i32i300i2−i2i2−i26−66−6000000000000000000000000000000
χ5744-4-4-444-4-20000-222-22-22−2i22i2−2i22i20000000000002i3−2i300i2−i2i2−i2−66−66000000000000000000000000000000
χ5844-4-4-444-4-20000-222-22-222i2−2i22i2−2i2000000000000−2i32i300−i2i2−i2i2−66−66000000000000000000000000000000
χ5944-4-4-444-4-20000-222-22-222i2−2i22i2−2i20000000000002i3−2i300−i2i2−i2i26−66−6000000000000000000000000000000
χ604-444-44-4-440000-44-444-4-4−2i22i22i2−2i20000000000000000−2i22i22i2−2i20000000000000000000000000000000000
χ614-444-44-4-440000-44-444-4-42i2−2i2−2i22i200000000000000002i2−2i2−2i22i20000000000000000000000000000000000
χ624-444-44-4-4-200002-22-2-222−2i22i22i2−2i20000000000000023−23i2−i2−i2i2i6−i6−i6i6000000000000000000000000000000
χ634-444-44-4-4-200002-22-2-222−2i22i22i2−2i200000000000000−2323i2−i2−i2i2−i6i6i6−i6000000000000000000000000000000
χ644-444-44-4-4-200002-22-2-2222i2−2i2−2i22i20000000000000023−23−i2i2i2−i2−i6i6i6−i6000000000000000000000000000000
χ654-444-44-4-4-200002-22-2-2222i2−2i2−2i22i200000000000000−2323−i2i2i2−i2i6−i6−i6i6000000000000000000000000000000
χ664-44-44-44-44-44-44-4-44-444-40000-4-44400000000000000000000000000000000000000000000000000
χ674-44-44-44-4-24-44-422-22-2-220000-2-22200004i−4i0000000000000000000000000000000000−2i2i00000000
χ684-44-44-44-4-24-44-422-22-2-220000-2-2220000−4i4i00000000000000000000000000000000002i−2i00000000
χ694-44-44-44-4-2-44-4422-22-2-22000022-2-200000000000000000000000000000000000000−2i32i30000000000
χ704-44-44-44-4-2-44-4422-22-2-22000022-2-2000000000000000000000000000000000000002i3−2i30000000000
χ714-4-44-4-44440000-44-4-4-444000000000000000000000000000000004-4000000000000000000000000
χ724-4-44-4-44440000-44-4-4-44400000000000000000000000000000000-44000000000000000000000000
χ734-4-4-444-44-244-4-422-2-222-20000-22-220000004i−4i00000000−2i−2i2i2i000000000000000000000000000000
χ744-4-4-444-44-244-4-422-2-222-20000-22-22000000−4i4i000000002i2i−2i−2i000000000000000000000000000000
χ754-4-4-444-44-2-4-44422-2-222-244-4-42-22-2000000000000-2-2220000000000000000000000000000000000
χ764-4-4-444-44-2-4-44422-2-222-2-4-4442-22-200000000000022-2-20000000000000000000000000000000000
χ77888-8-8-8-88-40000-4444-44-40000000000000000000000000000000000000000000000000000000000
χ788-8-88-8-888-400004-4444-4-40000000000000000000000000000000000000000000000000000000000

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