Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11247 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11248 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #387 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1441 |
| prime radical | C24×C11 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
604 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)(12,13,17,21,18,23,16,22)(14,24,27,36,28,35,26,19)(15,29,31,39,33,38,32,20)(25,34,30,37,41,43,42,40);(12,14,16,26,18,28,17,27)(13,19,21,24,23,36,22,35)(15,30,31,41,33,42,32,25)(20,37,38,34,39,40,29,43);(12,15,16,31,18,33,17,32)(13,20,21,38,23,39,22,29)(14,25,26,30,28,41,27,42)(19,34,24,40,36,43,35,37)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4236);