Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1909 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C23×C42 |
| direct product | C11×#10948 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C23×D4×C11 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1074 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,24,27,22)(19,28)(20,29)(21,23)(25,26,31,30);(12,13,14,15)(16,18)(17,22)(19,25)(20,30)(21,27)(23,24)(26,28)(29,31);(16,19,28,17,21,29,20,23)(18,25,26,22,27,31,30,24)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3936);