Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#21517 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C2×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C11×#3035 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ C2×C4×C8×C11 ◁ G | |
922 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,20,24,21,18,25,23)(19,22,27,30,28,26,31,29);(12,13,14,15);(16,18)(17,21)(19,26)(20,23)(22,28)(24,25)(27,29)(30,31);(16,19,20,27,21,28,25,31)(17,22,24,30,18,26,23,29)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14505);