Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#18091 |
| 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 | C11×#3169 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C11×#431 ◁ G | |
644 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)(12,13,16,19)(14,21,22,18)(15,17,24,20)(23,26,27,25)(28,29,32,36,33,30,37,35)(31,38,39,42,40,34,41,43);(13,17)(15,24)(18,25)(19,20)(21,26)(23,27)(28,30)(29,33)(31,38)(32,35)(34,40)(36,37)(39,42)(41,43);(12,14)(13,18)(15,23)(16,22)(17,25)(19,21)(20,26)(24,27)(28,31,37,41,33,40,32,39)(29,34,35,42,30,38,36,43);(13,19)(14,22)(17,20)(23,27)(29,30)(34,38)(35,36)(42,43)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11079);