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) = C26 |
| direct product | C11×#11029 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | #121 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G | |
1242 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(20,21,25,31,26,29,24,30)(22,32,35,43,36,27,34,44)(23,37,40,46,41,28,39,47)(33,42,49,51,50,48,38,45);(13,15)(16,17)(18,19)(20,22,26,36)(21,27,29,32)(23,38,41,49)(24,35,25,34)(28,45,37,51)(30,44,31,43)(33,40,50,39)(42,47,48,46);(17,19)(20,23,26,41)(21,28,29,37)(22,33,36,50)(24,40,25,39)(27,42,32,48)(30,47,31,46)(34,49,35,38)(43,51,44,45)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4017);