Finite Group Databasebeta

← Group #10855152

Character table — Group #10855152

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order1222222234444666666644121212124444444888812121212242424242424242422444444442661212121212122444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-11111-1-1111-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111
χ5111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1-1111-1-111-1-1-1-11
χ6111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111-111-1-11111-1
χ7111111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1
χ8111111111111111111111111111-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ911111111111111111111-1-11111-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-111-1-111-1111111-1-1-1
χ1011111111111111111111-1-11111-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-111-1-1111-1-1-1-1-1-1111
χ1111111111111111111111-1-11111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111111-1-1-1-1-111-1-1-1-1111
χ1211111111111111111111-1-11111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-11111111-1-1-1-11-1-11111-1-1-1
χ1311111111111111111111-1-11111-1-1-11111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-11111-1-1-111-1-111-1
χ1411111111111111111111-1-11111-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-11111111-1-111-1-11
χ1511111111111111111111-1-11111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1111-1-111-1-1-1-1-1-1-111-1-11
χ1611111111111111111111-1-11111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-111111-1-111-1
χ17222222222-2-2-2-2222222222-2-2-2-2-2000000000022-2-200000000220000-2-2-2-20000000002000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2000000000022-2-200000000-2-200002222000000000-2000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-220000000000-2-22200000000220000-2-222000000000-2000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-220000000000-2-22200000000-2-2000022-2-20000000002000000000
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
χ2922-22-22-2-22-22-2222-22-2-2-200-2-222000002i−2i0000000000000000002i2i−2i−2i000000000002i−2i00000002-20
χ3022-22-22-2-22-22-2222-22-2-2-200-2-222000002i−2i000000000000000000−2i−2i2i2i000000000002i−2i0000000-220
χ3122-22-22-2-22-22-2222-22-2-2-200-2-22200000−2i2i0000000000000000002i2i−2i−2i00000000000−2i2i0000000-220
χ3222-22-22-2-22-22-2222-22-2-2-200-2-22200000−2i2i000000000000000000−2i−2i2i2i00000000000−2i2i00000002-20
χ332-22-2-222-222-2-22-2-2-2222-2002-22-20002i−2i0000000000000000002-22i−2i2i−2i2-200000002i−2i000000000000
χ342-22-2-222-222-2-22-2-2-2222-2002-22-20002i−2i000000000000000000-22−2i2i−2i2i-2200000002i−2i000000000000
χ352-22-2-222-222-2-22-2-2-2222-2002-22-2000−2i2i0000000000000000002-2−2i2i−2i2i2-20000000−2i2i000000000000
χ362-22-2-222-222-2-22-2-2-2222-2002-22-2000−2i2i000000000000000000-222i−2i2i−2i-220000000−2i2i000000000000
χ372-22-2-222-22-222-2-2-2-2222-200-22-2202i−2i000000000000000000002-20000-22000002i−2i000002i−2i0000000
χ382-22-2-222-22-222-2-2-2-2222-200-22-2202i−2i00000000000000000000-2200002-2000002i−2i00000−2i2i0000000
χ392-22-2-222-22-222-2-2-2-2222-200-22-220−2i2i000000000000000000002-20000-2200000−2i2i00000−2i2i0000000
χ402-22-2-222-22-222-2-2-2-2222-200-22-220−2i2i00000000000000000000-2200002-200000−2i2i000002i−2i0000000
χ412-2-2-222-222-2-222-2-222-2-2200-222-20000000002-20000000022-2-2002-2-2200000000000000002-200000
χ422-2-2-222-222-2-222-2-222-2-2200-222-20000000002-20000000022-2-200-222-20000000000000000-2200000
χ432-2-2-222-222-2-222-2-222-2-2200-222-2000000000-2200000000-2-222002-2-220000000000000000-2200000
χ442-2-2-222-222-2-222-2-222-2-2200-222-2000000000-2200000000-2-22200-222-200000000000000002-200000
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
χ47444-44-4-4-4400004-44-44-4-40000000000000000000000000000000000000000000000000000022−22000
χ48444-44-4-4-4400004-44-44-4-400000000000000000000000000000000000000000000000000000−2222000
χ4944-44-44-4-444-44-444-44-4-4-40044-4-40000000000000000000000000000000000000000000000000000
χ5044-44-44-4-4-24-44-4-2-22-222200-2-2220000000000000000000000000000000000−2i32i30000000000000000
χ5144-44-44-4-4-24-44-4-2-22-222200-2-22200000000000000000000000000000000002i3−2i30000000000000000
χ5244-44-44-4-4-2-44-44-2-22-22220022-2-2000004i−4i000000000000000000000000000000000−2i2i0000000000
χ5344-44-44-4-4-2-44-44-2-22-22220022-2-200000−4i4i0000000000000000000000000000000002i−2i0000000000
χ5444-4-4-4-444400004-4-4-4-4444-40000000000000004-4000000000000000000000000000000000000000
χ5544-4-4-4-444400004-4-4-4-444-44000000000000000-44000000000000000000000000000000000000000
χ5644-4-4-4-444-20000-22222-2-24-4000000000000000-2200i6i6−i6−i6i6−i6i6−i600000000000000000000000000000
χ5744-4-4-4-444-20000-22222-2-24-4000000000000000-2200−i6−i6i6i6−i6i6−i6i600000000000000000000000000000
χ5844-4-4-4-444-20000-22222-2-2-440000000000000002-200i6i6−i6−i6−i6i6−i6i600000000000000000000000000000
χ5944-4-4-4-444-20000-22222-2-2-440000000000000002-200−i6−i6i6i6i6−i6i6−i600000000000000000000000000000
χ604-444-4-4-4440000-44-4-44-44000000000000022−2200000022−2222−22000000000000000000000000000000000
χ614-444-4-4-4440000-44-4-44-440000000000000−2222000000−2222−2222000000000000000000000000000000000
χ624-444-4-4-44-200002-222-22-2000000000000022−220000−2i32i3−22−22i6−i6−i6i600000000000000000000000000000
χ634-444-4-4-44-200002-222-22-2000000000000022−2200002i3−2i3−22−22−i6i6i6−i600000000000000000000000000000
χ644-444-4-4-44-200002-222-22-20000000000000−22220000−2i32i32−22−2−i6i6i6−i600000000000000000000000000000
χ654-444-4-4-44-200002-222-22-20000000000000−222200002i3−2i32−22−2i6−i6−i6i600000000000000000000000000000
χ664-44-4-444-4-24-4-44222-2-2-2200-22-220004i−4i000000000000000000000000000000000−2i2i000000000000
χ674-44-4-444-4-24-4-44222-2-2-2200-22-22000−4i4i0000000000000000000000000000000002i−2i000000000000
χ684-44-4-444-4-2-444-4222-2-2-22002-22-204i−4i000000000000000000000000000000000−2i2i00000000000000
χ694-44-4-444-4-2-444-4222-2-2-22002-22-20−4i4i0000000000000000000000000000000002i−2i00000000000000
χ704-4-444-44-440000-444-4-44-400000000000000000000000000000000000004i−4i0000000000000000000
χ714-4-444-44-440000-444-4-44-40000000000000000000000000000000000000−4i4i0000000000000000000
χ724-4-4-444-44444-4-4-4-444-4-44004-4-440000000000000000000000000000000000000000000000000000
χ734-4-4-444-44-244-4-422-2-222-200-222-2000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ744-4-4-444-44-244-4-422-2-222-200-222-20000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ754-4-4-444-44-2-4-44422-2-222-2002-2-220000000004-400000000-2-22200000000000000000000000000000
χ764-4-4-444-44-2-4-44422-2-222-2002-2-22000000000-440000000022-2-200000000000000000000000000000
χ77888-88-8-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000
χ788-8-888-88-8-400004-4-444-440000000000000000000000000000000000000000000000000000000000

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