Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#13137 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #459 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C2×C11 | #1925 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
316 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,21,18,23,15,19)(14,24,27,39,28,42,25,41)(16,30,32,40,33,35,29,22)(20,36,37,43,38,31,34,26);(13,19,23,21)(20,34,38,37)(22,35,40,30)(24,41,42,39);(12,14,15,25,18,28,17,27)(13,20,21,37,23,38,19,34)(16,31,29,43,33,36,32,26)(22,39,30,42,40,41,35,24)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6125);