Finite Group Databasebeta

← Group #10691559

Character table — Group #10691559

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order122222344444466666664444444121212121212121244888812121212121212121212242424242424242488884412121212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-11-1-1111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111-1-11-1-1111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-11-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-11-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1
χ91111111-111-1-1-11111111-1111-1-1-1-1-1-1-111111-111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−i1-111-1-1i−iii−i−iii−i−ii−i
χ101111111-111-1-1-11111111-1111-1-1-1-1-1-1-111111-111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii1-111-1-1−ii−i−iii−i−iii−ii
χ111111111-111-1-1-11111111-1111-1-1-1-1-1-1-111111-1-1-111-1-11111-1-1-1-1-1-1-1-11111ii−i−i-11-1-111i−iii−i−i−i−iii−ii
χ121111111-111-1-1-11111111-1111-1-1-1-1-1-1-111111-1-1-111-1-11111-1-1-1-1-1-1-1-11111−i−iii-11-1-111−ii−i−iiiii−i−ii−i
χ131111111-111-1-1-11111111-1-1-1111-1-1-1-1-11111-1111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i-11-1-111i−i−i−iiiii−i−i−ii
χ141111111-111-1-1-11111111-1-1-1111-1-1-1-1-11111-1111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iii-11-1-111−iiii−i−i−i−iiii−i
χ151111111-111-1-1-11111111-1-1-1111-1-1-1-1-11111-11-1-111-1-1-1-1-1-11111-1-1-1-11111ii−i−i1-111-1-1i−i−i−iii−i−iiii−i
χ161111111-111-1-1-11111111-1-1-1111-1-1-1-1-11111-11-1-111-1-1-1-1-1-11111-1-1-1-11111−i−iii1-111-1-1−iiii−i−iii−i−i−ii
χ1722222222-2-22222222222-200-200-22222-2-2-2-2000000-2-200000000000000002222000000-2-20000000000
χ1822222222-2-22222222222-200-200-22222-2-2-2-2000000-2-20000000000000000-2-2-2-2000000220000000000
χ192222222-2-2-2-2-2-22222222200-2002-2-2-2-2-2-2-2-20000002200000000000000002i2i−2i−2i000000−2i2i0000000000
χ202222222-2-2-2-2-2-22222222200-2002-2-2-2-2-2-2-2-2000000220000000000000000−2i−2i2i2i0000002i−2i0000000000
χ21222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-12-2-22-2-22-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-12-2-22-2-22-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-1000000000000
χ25222222-1-222-2-2-2-1-1-1-1-1-1-1-2222-2-2-21111-1-1-1-12-222-2-211-1-1-1-11111-1-1-1-1111100002-2-1-111000000000000
χ26222222-1-222-2-2-2-1-1-1-1-1-1-1-2222-2-2-21111-1-1-1-12-2-2-22211-1-1-1-111111111-1-1-1-10000-2211-1-1000000000000
χ27222222-1-222-2-2-2-1-1-1-1-1-1-1-2-2-2222-21111-1-1-1-1-2222-2-2111111-1-1-1-1-1-1-1-111110000-2211-1-1000000000000
χ28222222-1-222-2-2-2-1-1-1-1-1-1-1-2-2-2222-21111-1-1-1-1-22-2-222111111-1-1-1-11111-1-1-1-100002-2-1-111000000000000
χ292222-2-22222-22-2-2-2-2-2222-222-2-2-2222-2-22-2-22-2200002-222-2-222-2-2000000000000000000000000000000
χ302222-2-22222-22-2-2-2-2-2222-2-2-2-222222-2-22-2-222-200002-2-2-222-2-222000000000000000000000000000000
χ312222-2-222-2-2-22-2-2-2-2-2222200200-222-2-2-222-2000000-2200000000000000000000000000002i−2i2i−2i000000
χ322222-2-222-2-2-22-2-2-2-2-2222200200-222-2-2-222-2000000-220000000000000000000000000000−2i2i−2i2i000000
χ332222-2-22-2222-22-2-2-2-2222222-222-2-2-2222-2-22-2-20000-2222-2-2-2-222000000000000000000000000000000
χ342222-2-22-2222-22-2-2-2-22222-2-2-2-2-2-2-2-2222-2-22220000-22-2-22222-2-2000000000000000000000000000000
χ352222-2-22-2-2-22-22-2-2-2-2222-2002002-2-222-222-20000002-200000000000000000000000000002-2-22000000
χ362222-2-22-2-2-22-22-2-2-2-2222-2002002-2-222-222-20000002-20000000000000000000000000000-222-2000000
χ372222-2-2-1222-22-21111-1-1-1-222-2-2-22-1-111-111-1-220000-11-1-111-1-111−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ382222-2-2-1222-22-21111-1-1-1-222-2-2-22-1-111-111-1-220000-11-1-111-1-111i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ392222-2-2-1222-22-21111-1-1-1-2-2-2-2222-1-111-111-12-20000-1111-1-111-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ402222-2-2-1222-22-21111-1-1-1-2-2-2-2222-1-111-111-12-20000-1111-1-111-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ412222-2-2-1-2222-221111-1-1-1222-222-211-1-1-111-1-2-200001-1-1-11111-1-1−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i3000000000000
χ422222-2-2-1-2222-221111-1-1-1222-222-211-1-1-111-1-2-200001-1-1-11111-1-1i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i3000000000000
χ432222-2-2-1-2222-221111-1-1-12-2-2-2-2-2-211-1-1-111-12200001-111-1-1-1-111−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i3000000000000
χ442222-2-2-1-2222-221111-1-1-12-2-2-2-2-2-211-1-1-111-12200001-111-1-1-1-111i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i3000000000000
χ4522-2-22-222002-2-222-2-22-2-200000002-22-20000002−22−200000000002−22−22−22−22-22-20000000000002−22−200
χ4622-2-22-222002-2-222-2-22-2-200000002-22-20000002−22−200000000002−22−22−22−2-22-22000000000000−22−2200
χ4722-2-22-222002-2-222-2-22-2-200000002-22-2000000−22−220000000000−22−22−22−222-22-2000000000000−22−2200
χ4822-2-22-222002-2-222-2-22-2-200000002-22-2000000−22−220000000000−22−22−22−22-22-220000000000002−22−200
χ4922-2-22-22-200-22222-2-22-2-20000000-22-220000002−2−2200000000002−22−2−22−222i−2i−2i2i000000000000i2−i2−i2i200
χ5022-2-22-22-200-22222-2-22-2-20000000-22-220000002−2−2200000000002−22−2−22−22−2i2i2i−2i000000000000−i2i2i2−i200
χ5122-2-22-22-200-22222-2-22-2-20000000-22-22000000−222−20000000000−22−222−22−22i−2i−2i2i000000000000−i2i2i2−i200
χ5222-2-22-22-200-22222-2-22-2-20000000-22-22000000−222−20000000000−22−222−22−2−2i2i2i−2i000000000000i2−i2−i2i200
χ53444444-24-4-4444-2-2-2-2-2-2-2-400-400-4-2-2-2-222220000002200000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-2-2-2-2-2400-400422222222000000-2-200000000000000000000000000000000000000
χ554444-4-4-24-4-4-44-42222-2-2-2400400-4-2-2222-2-220000002-200000000000000000000000000000000000000
χ564444-4-4-2-4-4-44-442222-2-2-2-400400422-2-22-2-22000000-2200000000000000000000000000000000000000
χ5744-4-44-4-24004-4-4-2-222-2220000000-22-2200000022−2222−220000000000−22−22−22−220000000000000000000000
χ5844-4-44-4-24004-4-4-2-222-2220000000-22-22000000−2222−222200000000002−22−22−22−20000000000000000000000
χ5944-4-44-4-2-400-444-2-222-22200000002-22-200000022−22−22220000000000−22−222−22−20000000000000000000000
χ6044-4-44-4-2-400-444-2-222-22200000002-22-2000000−222222−2200000000002−22−2−22−220000000000000000000000
χ6144-4-4-444400-4-44-4-4444-4-400000004-4-4400000000000000000000000000000000000000000000000000
χ6244-4-4-444-40044-4-4-4444-4-40000000-444-400000000000000000000000000000000000000000000000000
χ6344-4-4-44-2400-4-4422-2-2-2220000000-222-200000000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000
χ6444-4-4-44-2400-4-4422-2-2-2220000000-222-200000000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000
χ6544-4-4-44-2-40044-422-2-2-22200000002-2-2200000000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000
χ6644-4-4-44-2-40044-422-2-2-22200000002-2-2200000000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000
χ674-4-4400404-40000000-4-4404i−4i00000000400-4000000004i−4i000000000000000000000000000000000000
χ684-4-4400404-40000000-4-440−4i4i00000000400-400000000−4i4i000000000000000000000000000000000000
χ694-4-440040-440000000-4-4400004-400000-4004000000000000004-4000000000000000000000000000000
χ704-4-440040-440000000-4-440000-4400000-400400000000000000-44000000000000000000000000000000
χ714-4-4400-204-4000−2i32i3−2i32i322-204i−4i00000000-2−2i32i3200000000−2i2i23−230000000000000000000000000000000000
χ724-4-4400-204-4000−2i32i3−2i32i322-20−4i4i00000000-2−2i32i32000000002i−2i−23230000000000000000000000000000000000
χ734-4-4400-204-40002i3−2i32i3−2i322-204i−4i00000000-22i3−2i3200000000−2i2i−23230000000000000000000000000000000000
χ744-4-4400-204-40002i3−2i32i3−2i322-20−4i4i00000000-22i3−2i32000000002i−2i23−230000000000000000000000000000000000
χ754-4-4400-20-44000−2i32i3−2i32i322-200004-40000022i3−2i3-2000000000000−2i32i3-22000000000000000000000000000000
χ764-4-4400-20-44000−2i32i3−2i32i322-20000-440000022i3−2i3-20000000000002i3−2i32-2000000000000000000000000000000
χ774-4-4400-20-440002i3−2i32i3−2i322-200004-4000002−2i32i3-20000000000002i3−2i3-22000000000000000000000000000000
χ784-4-4400-20-440002i3−2i32i3−2i322-20000-44000002−2i32i3-2000000000000−2i32i32-2000000000000000000000000000000
χ798-88-80080000000000-88-80000000000000000000000000000000000000000000000000000000000000
χ808-88-800-4000000−4i34i34i3−4i34-440000000000000000000000000000000000000000000000000000000000000
χ818-88-800-40000004i3−4i3−4i34i34-440000000000000000000000000000000000000000000000000000000000000

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