Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11541 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#13219 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#99 |
| commutator | C24 | C22×C4×C11 |
| Frattini, cosocle | C22×D4 | C23×C11 |
| prime radical | C2×C11×#120 | C22 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×D4×C11 ◁ G | |
624 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 352 |
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)(18,24,27,31)(19,28,25,23)(20,22)(21,26)(29,30);(16,18,25,26,20,27,19,29)(17,21,28,31,22,30,23,24);(12,13,14,15)(17,22)(21,30)(23,28)(24,31)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6207);