Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18452 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1028 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,18)(14,22)(15,26)(19,32)(20,30)(21,27)(23,25)(24,39)(28,41)(31,36)(33,43)(34,40)(35,42)(37,38);(12,13,16,21)(14,19,23,33)(15,27,26,18)(17,20,29,35)(22,36,25,34)(24,40,38,31)(28,42,41,30)(32,37,43,39);(14,23)(15,28)(18,30)(19,33)(22,25)(24,37)(26,41)(27,42)(31,32)(34,36)(38,39)(40,43);(12,14,16,23)(13,19,21,33)(15,24,26,38)(17,25,29,22)(18,31,27,40)(20,34,35,36)(28,39,41,37)(30,43,42,32)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11440);