Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61038 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C22×C11 | C23×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C4×D4×C11 ◁ G | |
2790 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17)(18,25)(19,23)(20,29)(21,24)(22,28)(26,27)(30,31);(16,18)(17,22)(19,28)(20,30)(21,26)(23,27)(24,31)(25,29);(13,15)(18,26)(22,31)(25,27)(28,30);(16,17)(18,27)(19,23)(20,29)(21,24)(22,30)(25,26)(28,31);(16,19,21,20)(17,23,24,29)(18,28,26,30)(22,27,31,25)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54026);