Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1366 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#11956 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #333 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C2×C11 | C2×#333 |
| prime radical | C23×C11 | #100 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
292 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,20,29,21,39,37,17,22,31,38,15,19,28,35)(14,23,26,36,24,34,30,42,25,40,41,43,27,18,32,33);(12,14,17,25)(13,18)(15,24,29,27)(16,30,31,32)(19,23)(20,36)(21,40)(22,34)(26,28,41,39)(33,37)(35,42)(38,43);(12,15,17,29)(13,19,22,21)(14,24,25,27)(16,28,31,39)(18,23,34,40)(20,35,38,37)(26,30,41,32)(33,36,42,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4944);