Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8325 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#10985 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #379 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1270 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,26)(19,30,32,23)(20,33)(21,25)(22,28)(24,35)(27,41,43,40)(29,39)(31,38,47,45)(34,37)(36,42,44,46);(12,13)(14,15)(16,18,21,29)(17,22,25,37)(19,27,32,43)(20,34,35,28)(23,36,30,44)(24,39,33,26)(31,46,47,42)(38,41,45,40);(13,15)(16,19)(17,23)(18,27)(20,31)(21,32)(22,36)(24,38)(25,30)(26,40)(28,42)(29,43)(33,45)(34,46)(35,47)(37,44)(39,41)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3973);