Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1795 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#10778 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #379 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | C22⋊#95 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
1164 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)(14,24,27,19)(15,29,31,37)(16,22)(17,23)(18,21)(20,30,36,32)(25,39)(26,35,28,34)(33,40)(38,42)(41,43);(12,14,17,28,18,27,16,26)(13,19,23,35,21,24,22,34)(15,25,30,40,31,41,32,42)(20,33,29,43,36,38,37,39);(12,15)(13,20)(14,25)(16,32)(17,30)(18,31)(19,33)(21,36)(22,37)(23,29)(24,38)(26,42)(27,41)(28,40)(34,39)(35,43)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3766);