Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11364 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #121 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #390 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
606 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)(14,19)(15,17)(16,18)(20,21)(22,30,33,26)(23,34,37,27)(24,29)(25,28)(31,41)(32,46,38,42)(35,43)(36,47,39,44)(40,45)(48,49)(50,51);(12,14,16,15)(13,17,18,19)(20,22)(21,26)(23,35)(24,38)(25,33)(27,43)(28,30)(29,46)(31,36)(32,40)(34,51)(37,50)(39,49)(41,44)(42,45)(47,48);(12,15,16,14)(13,17,18,19)(20,23)(21,27)(22,31)(24,39)(25,37)(26,41)(28,34)(29,47)(30,48)(32,50)(33,49)(35,38)(36,40)(42,51)(43,46)(44,45)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4352);