Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(7,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4×C11 · Schur multiplier (H2) = C214 |
| direct product | C11×#62654 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C26 |
| commutator | C2 | C25×C4×C11 |
| Frattini, cosocle | C22 | C26×C11 |
| prime radical | C2×C11×#585 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
11222 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 6 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(16,17)(18,22)(19,26)(20,21)(23,27)(24,28)(25,31)(29,30);(17,21)(22,28)(23,26)(29,31);(18,24)(22,28)(25,30)(29,31);(16,18)(17,22)(19,25)(20,24)(21,28)(23,29)(26,31)(27,30);(16,17)(18,22)(19,23)(20,21)(24,28)(25,29)(26,27)(30,31);(16,19,20,27)(17,23,21,26)(18,25,24,30)(22,29,28,31)1430 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 55642);