Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2215 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#12907 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C2×D8 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
342 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,18,19)(20,21)(22,30)(23,35)(24,27)(25,38)(26,32)(28,31)(29,36)(33,42)(34,49)(37,50)(39,48)(40,51)(41,46)(43,45)(44,47);(20,22,31,45,25,34,37,48,24,33,46,51,36,47,23,32)(21,26,35,44,29,40,41,42,27,39,50,49,38,43,28,30);(12,13,14,15)(21,27)(26,39)(28,41)(29,38)(30,42)(35,50)(40,43)(44,49)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5895);