Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7943 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#7969 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#95 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C24×C11 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C42×C11 ◁ G | |
520 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,20,17,21,16,19)(14,22,24,18,23,27,25,26)(28,29)(30,38,41,42)(31,35)(32,36)(33,37)(34,40,43,39);(12,14,16,25,17,23,15,24)(13,18,20,27,21,26,19,22)(28,30)(29,34,37,43)(31,39)(32,40)(33,41)(35,42,36,38);(14,23)(18,26)(22,27)(24,25)(28,31,33,32)(29,35,37,36)(30,39,41,40)(34,42,43,38)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 957);