Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8465 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#8475 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #379 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C11×#3500 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
932 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,17,15,16,18,19)(20,21)(22,30)(23,34,36,27)(24,37)(25,29)(26,32)(28,40)(31,46,48,51)(33,44)(35,43,39,45)(38,42)(41,47,50,49);(13,16)(14,18)(20,22)(21,26)(23,31)(24,38)(25,33)(27,41)(28,44)(29,42)(30,37)(32,40)(34,50)(35,49)(36,48)(39,47)(43,46)(45,51);(13,16)(14,18)(20,23)(21,27)(22,31)(24,39)(25,36)(26,41)(28,45)(29,34)(30,46)(32,49)(33,48)(35,40)(37,43)(38,47)(42,50)(44,51)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1463);