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×#13044 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C11 |
| Frattini, cosocle | C22×D4 | C23×C11 |
| prime radical | C2×C11×H(5,𝔽2) | C22 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C11 ◁ C22×D4×C11 ◁ G | |
724 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17)(18,24,25,30)(19,22,27,29)(20,23)(21,26)(28,31);(12,13,14,15)(18,25)(21,28)(22,29)(26,31);(16,18,20,25)(17,21,23,28)(19,26,27,31)(22,24,29,30)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6032);