Finite Group Databasebeta

← Group #10844668

Character table — Group #10844668

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order1222222234444666666644121212124444444888812121212242424242424242444444444442661212121212124444488882
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-11111-1-11-1-111-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111111
χ5111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1-111-1-1-1111111-1
χ6111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111-1-1-1-1-1-11
χ7111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ8111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1
χ911111111111111111111-1-11111-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-111-1-111-111-1-111-1-1-1
χ1011111111111111111111-1-11111-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1111-1-111-1-1111
χ1111111111111111111111-1-11111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1111
χ1211111111111111111111-1-11111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1-1-11111111-1-1-1
χ1311111111111111111111-1-11111-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-11
χ1411111111111111111111-1-11111-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-11111-11111-1-111-1
χ1511111111111111111111-1-11111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1-111-1-1111-1-1-1-111-1
χ1611111111111111111111-1-11111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-11111-1-11
χ17222222222-2-2-2-2222222222-2-2-2-2-2000000000022-2-20000000000002222-2-2000000000-2000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2000000000022-2-2000000000000-2-2-2-2220000000002000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-220000000000-2-22200000000000022-2-222000000000-2000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-220000000000-2-222000000000000-2-222-2-20000000002000000000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-122222-2-2-2-2-2-2-1-1-1-1111111110000000000-211-1-1-1-1110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-12-2-2-2-222-2-2-2-2-1-1-1-11111111100000000002-1-11111-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-122-1-1-1-12-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2111111110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-222-2-22222-2-21111-1-1-1-111110000000000-211-1-111-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-222-2-2-2-2-2-22211111111-1-1-1-100000000002-1-1-1-111110000000000
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
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222-2-222-2-21111-1-1-1-1111100000000002-1-111-1-1110000000000
χ2922-22-22-2-222-2-2222-22-2-2-2002-2-22000002i−2i000000000000000022-2-200000000000002i−2i000002i−2i000
χ3022-22-22-2-222-2-2222-22-2-2-2002-2-22000002i−2i0000000000000000-2-22200000000000002i−2i00000−2i2i000
χ3122-22-22-2-222-2-2222-22-2-2-2002-2-2200000−2i2i000000000000000022-2-20000000000000−2i2i00000−2i2i000
χ3222-22-22-2-222-2-2222-22-2-2-2002-2-2200000−2i2i0000000000000000-2-2220000000000000−2i2i000002i−2i000
χ332-22-222-2-222-22-2-2-2-2222-20022-2-200000002i−2i0000002i2i−2i−2i00002i−2i2i−2i00000000000000002-20000000
χ342-22-222-2-222-22-2-2-2-2222-20022-2-200000002i−2i0000002i2i−2i−2i0000−2i2i−2i2i0000000000000000-220000000
χ352-22-222-2-222-22-2-2-2-2222-20022-2-20000000−2i2i000000−2i−2i2i2i00002i−2i2i−2i0000000000000000-220000000
χ362-22-222-2-222-22-2-2-2-2222-20022-2-20000000−2i2i000000−2i−2i2i2i0000−2i2i−2i2i00000000000000002-20000000
χ372-2-2-2-2222222-2-2-2-222-2-22002-22-202i−2i000000000000000000002i−2i−2i2i002-22-20002i−2i00000000000000
χ382-2-2-2-2222222-2-2-2-222-2-22002-22-202i−2i00000000000000000000−2i2i2i−2i00-22-220002i−2i00000000000000
χ392-2-2-2-2222222-2-2-2-222-2-22002-22-20−2i2i000000000000000000002i−2i−2i2i00-22-22000−2i2i00000000000000
χ402-2-2-2-2222222-2-2-2-222-2-22002-22-20−2i2i00000000000000000000−2i2i2i−2i002-22-2000−2i2i00000000000000
χ412-2-2-2-22222-2-222-2-222-2-2200-22-220002-20000000000000000000000002-2-22000002-2000002-200000
χ422-2-2-2-22222-2-222-2-222-2-2200-22-220002-2000000000000000000000000-222-2000002-200000-2200000
χ432-2-2-2-22222-2-222-2-222-2-2200-22-22000-220000000000000000000000002-2-2200000-2200000-2200000
χ442-2-2-2-22222-2-222-2-222-2-2200-22-22000-22000000000000000000000000-222-200000-22000002-200000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-2442222-40000000000-2-2220000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-422224000000000022-2-20000000000000000000000000000000000000
χ47444-4-4-44-4400004-4-4-44-440000000000000000000000000000000000000000000000000000000−2i22i20
χ48444-4-4-44-4400004-4-4-44-4400000000000000000000000000000000000000000000000000000002i2−2i20
χ4944-44-44-4-44-444-444-44-4-4-400-444-40000000000000000000000000000000000000000000000000000
χ5044-44-44-4-4-24-4-44-2-22-222200-222-2000004i−4i000000000000000000000000000000000−2i2i0000000000
χ5144-44-44-4-4-24-4-44-2-22-222200-222-200000−4i4i0000000000000000000000000000000002i−2i0000000000
χ5244-44-44-4-4-2-444-4-2-22-2222002-2-220000000000000000000000000000000000−2i32i30000000000000000
χ5344-44-44-4-4-2-444-4-2-22-2222002-2-2200000000000000000000000000000000002i3−2i30000000000000000
χ5444-4-44-4-44400004-44-4-44-44i−4i0000000000000004i−4i000000000000000000000000000000000000000
χ5544-4-44-4-44400004-44-4-44-4−4i4i000000000000000−4i4i000000000000000000000000000000000000000
χ5644-4-44-4-44-20000-22-222-224i−4i000000000000000−2i2i006−66−6i6i6−i6−i600000000000000000000000000000
χ5744-4-44-4-44-20000-22-222-224i−4i000000000000000−2i2i00−66−66−i6−i6i6i600000000000000000000000000000
χ5844-4-44-4-44-20000-22-222-22−4i4i0000000000000002i−2i006−66−6−i6−i6i6i600000000000000000000000000000
χ5944-4-44-4-44-20000-22-222-22−4i4i0000000000000002i−2i00−66−66i6i6−i6−i600000000000000000000000000000
χ604-444-4-4-4440000-444-44-4-40000000000000000000000000000000004i−4i00000000000000000000000
χ614-444-4-4-4440000-444-44-4-4000000000000000000000000000000000−4i4i00000000000000000000000
χ624-44-444-4-44-44-44-4-4-4444-400-4-4440000000000000000000000000000000000000000000000000000
χ634-44-444-4-4-24-44-4222-2-2-2200-2-22200000004i−4i000000−2i−2i2i2i000000000000000000000000000000000
χ644-44-444-4-4-24-44-4222-2-2-2200-2-2220000000−4i4i0000002i2i−2i−2i000000000000000000000000000000000
χ654-44-444-4-4-2-44-44222-2-2-220022-2-20000000000000000000−2i32i3−2i32i300000000000000000000000000000
χ664-44-444-4-4-2-44-44222-2-2-220022-2-200000000000000000002i3−2i32i3−2i300000000000000000000000000000
χ674-4-444-44-440000-44-4-4-44400000000000000022−220000000022−22−222200000000000000000000000000000
χ684-4-444-44-440000-44-4-4-444000000000000000−222200000000−222222−2200000000000000000000000000000
χ694-4-444-44-4-200002-2222-2-200000000000000022−2200−2i32i3i6−i6−i6i6−222−200000000000000000000000000000
χ704-4-444-44-4-200002-2222-2-200000000000000022−22002i3−2i3−i6i6i6−i6−222−200000000000000000000000000000
χ714-4-444-44-4-200002-2222-2-2000000000000000−222200−2i32i3−i6i6i6−i62−2−2200000000000000000000000000000
χ724-4-444-44-4-200002-2222-2-2000000000000000−2222002i3−2i3i6−i6−i6i62−2−2200000000000000000000000000000
χ734-4-4-4-4444-244-4-422-2-222-200-22-2204i−4i000000000000000000000000000000000−2i2i00000000000000
χ744-4-4-4-4444-244-4-422-2-222-200-22-220−4i4i0000000000000000000000000000000002i−2i00000000000000
χ754-4-4-4-4444-2-4-44422-2-222-2002-22-20004-4000000000000000000000000000000000-22000000000000
χ764-4-4-4-4444-2-4-44422-2-222-2002-22-2000-440000000000000000000000000000000002-2000000000000
χ77888-8-8-88-8-40000-4444-44-40000000000000000000000000000000000000000000000000000000000
χ788-888-8-8-88-400004-4-44-4440000000000000000000000000000000000000000000000000000000000

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