Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7453 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#7453 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #1365 |
| commutator | C2×C16 | C2×C4×C11 |
| Frattini, cosocle | C4×C16 | C22×C11 |
| prime radical | C22×C11 | #361 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C4×C8×C11 ◁ C4×C11×C16 ◁ G | |
102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 2 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,22,17,35,14,26,16,34,27,38,28,43,29,21,19,25,33,20,37,24,31,42,18,23,32,41,36,39,30,40);(13,20,25,22)(14,27)(15,29)(16,18)(17,36)(21,24,40,35)(23,41,34,38)(26,39,42,43)(28,37)(30,33)(31,32)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 441);