Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13103 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #1898 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C2×#41 | C23×C11 |
| prime radical | C11×#3010 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C2×C11×2−1+4 ◁ G | |
646 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,18,23,19,24,17,22)(14,16,21,34,27,35,36,25)(15,28,31,20,32,38,30,39)(26,41,37,29,42,43,40,33);(12,14,25,13)(15,26,41,20)(16,23,17,36)(18,21,35,22)(19,27,34,24)(28,31,37,33)(29,38,30,40)(32,42,43,39);(12,15,19,32)(13,20,24,39)(14,26,27,42)(16,33,35,29)(17,31,18,30)(21,40,36,37)(22,38,23,28)(25,41,34,43)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6091);