Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3198 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#17953 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C42 | C24×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C23×C11 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C11×#431 ◁ G | |
558 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,19,16,18,22,25)(14,17,21,24,20,23,26,27)(28,29,33,36,34,30,32,38)(31,35,41,42,39,37,40,43);(14,20)(17,23)(21,26)(24,27)(28,30,34,29)(31,35,39,37)(32,36,33,38)(40,43,41,42);(12,14,15,21,16,20,22,26)(13,17,19,24,18,23,25,27)(28,31,32,40,34,39,33,41)(29,35,38,43,30,37,36,42);(13,18)(17,23)(19,25)(24,27)(31,39)(35,37)(40,41)(42,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 10941);