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×#22899 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | D42 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | #2358 |
| prime radical | C11×#3018 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G | |
1016 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 176 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,22,19,23,18,21)(14,24,26,27,16,15,25,20);(12,14,17,26,19,16,18,25)(13,20,22,24,23,27,21,15);(12,15)(13,14)(16,23)(17,20)(18,27)(19,24)(21,25)(22,26);(12,16)(13,15)(14,19)(17,25)(18,26)(20,22)(21,27)(23,24)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15887);