Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11150 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #124 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #397 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
818 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)(18,27)(19,31,35,45)(20,36)(21,25)(22,26)(23,29)(24,34,42,33)(28,38,32,41)(30,39)(37,40)(43,44,47,46);(12,13)(14,15)(16,18)(17,23)(19,32)(20,37)(21,29)(22,30)(24,41)(25,39)(26,40)(27,36)(28,35)(31,43)(33,44)(34,46)(38,42)(45,47);(13,15)(16,19,20,33,22,35,21,34)(17,24,25,31,26,42,36,45)(18,28,29,44,30,32,37,46)(23,38,27,43,40,41,39,47)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4138);