Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11393 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #379 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
850 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)(20,21,25,29,26,30,24,37)(22,31,33,27,34,42,38,41)(23,28,35,44,36,45,39,43)(32,47,50,51,49,46,48,40);(12,13,15,17)(14,18,19,16)(20,22)(21,27)(23,32)(24,38)(25,33)(26,34)(28,40)(29,42)(30,41)(31,37)(35,50)(36,49)(39,48)(43,46)(44,47)(45,51);(12,14,15,19)(13,16,17,18)(20,23)(21,28)(22,32)(24,39)(25,35)(26,36)(27,40)(29,44)(30,45)(31,46)(33,50)(34,49)(37,43)(38,48)(41,51)(42,47)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4381);