Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1595 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#8409 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | #379 |
| prime radical | C11×#3449 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G | |
972 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)(12,13,15,17,16,19,14,18)(20,21,24,29,25,28,39,43)(22,30,33,44,32,26,37,41)(23,34,36,45,35,27,38,42)(31,46,48,51,47,40,49,50);(13,17)(14,15)(18,19)(20,22)(21,26)(23,31)(24,37)(25,32)(27,40)(28,30)(29,44)(33,39)(34,46)(35,47)(36,49)(38,48)(41,43)(42,51)(45,50);(20,23)(21,27)(22,31)(24,38)(25,35)(26,40)(28,34)(29,45)(30,46)(32,47)(33,49)(36,39)(37,48)(41,51)(42,43)(44,50)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1397);