Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17411 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#17422 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#120 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C4×D4×C11 ◁ G | |
1060 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,20,17,21,27,35)(14,19,23,33,25,34,38,43)(16,18,26,30,28,31,39,41)(22,32,36,42,24,29,37,40);(13,18)(15,26)(19,29)(21,31)(23,37)(27,39)(32,34)(36,38);(12,14,16,24)(13,19,18,29)(15,23,26,37)(17,25,28,22)(20,33,30,40)(21,34,31,32)(27,38,39,36)(35,43,41,42);(14,22)(19,32)(23,36)(24,25)(29,34)(33,42)(37,38)(40,43)605 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 10410);