Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23876 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23880 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3489 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1696 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)(16,17,23,27)(18,28,20,31)(19,30,24,29)(21,26,22,25);(12,13)(14,15)(16,18)(17,19)(20,23)(21,30)(22,29)(24,27)(25,31)(26,28);(13,15)(16,19,23,24)(17,20,27,18)(21,28,22,31)(25,30,26,29);(16,20)(17,24)(18,23)(19,27)(21,29)(22,30)(25,28)(26,31)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16868);