Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8412 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#8413 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #379 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C11×#3518 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
702 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)(13,16,17,18)(20,21)(22,30,33,26)(23,34,36,43)(24,29)(25,28)(27,35,41,37)(31,46)(32,45,50,40)(38,42)(39,47)(44,49)(48,51);(12,13)(14,18)(15,17)(16,19)(20,22)(21,26)(23,31)(24,32)(25,33)(27,39)(28,30)(29,40)(34,51)(35,47)(36,48)(37,49)(38,50)(41,44)(42,45)(43,46);(20,23,25,36)(21,27,28,41)(22,31,33,48)(24,37,38,35)(26,39,30,44)(29,43,42,34)(32,49,50,47)(40,46,45,51)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1401);