Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2199 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13046 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C11 |
| Frattini, cosocle | C2×#41 | C23×C11 |
| socle | C2×C11 | #1889 |
| prime radical | C11×#3025 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C2×C4×C11 ◁ C2×C11×#41 ◁ G | |
644 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)(12,13,16,20,17,21,28,34)(14,22,26,36,24,35,39,43)(15,19,23,30,27,33,37,41)(18,29,32,38,31,40,42,25);(12,14,23,29,17,24,37,40)(13,18,30,36,21,31,41,43)(15,25,16,26,27,38,28,39)(19,22,20,32,33,35,34,42);(14,24)(15,27)(16,28)(18,31)(22,35)(29,40)(32,42)(36,43)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6034);