Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#22897 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | D42 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#453 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G | |
1074 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17)(18,27)(19,23)(20,25)(21,24)(22,26)(28,31)(29,30);(12,14,15,13)(16,18,22,28)(17,19,26,29)(20,30,21,23)(24,31,25,27);(16,19,22,29)(17,18,26,28)(20,27,21,31)(23,25,30,24);(16,19)(17,23)(18,24)(20,31)(21,27)(22,29)(25,28)(26,30)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15885);