Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3198 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#21843 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G | |
970 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(16,17)(18,24)(19,22)(20,23)(21,26)(25,30)(27,29)(28,31)(32,33)(34,37)(35,38)(36,40)(39,43)(41,45)(42,44)(46,47);(16,18,20,26)(17,21,23,24)(19,27,28,25)(22,30,31,29)(32,34)(33,37)(35,42)(36,41)(38,44)(39,46)(40,45)(43,47);(16,19,20,28)(17,22,23,31)(18,25,26,27)(21,29,24,30)(33,38)(35,43)(37,44)(39,40)(42,47)(45,46);(17,23)(21,24)(22,31)(29,30)(34,41)(37,45)(42,47)(44,46)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14831);