Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7694 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#9115 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C25×C11 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G | |
952 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(17,20)(18,22)(21,23)(24,25)(26,28,30,31)(27,29);(16,17,18,20,19,21,22,23)(24,26)(25,28,29,31)(27,30);(13,15)(17,21)(20,23)(26,30)(28,31)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2103);