Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#12036 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×D8 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C22×C11 | C2×#107 |
| prime radical | C23×C11 | #107 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
212 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,18,16,19,22,25)(14,17,21,24,20,23,26,27)(28,29)(30,38)(31,35)(32,41)(33,43)(34,37)(36,39)(40,42);(12,14)(13,17)(15,21)(16,20)(18,24)(19,23)(22,26)(25,27)(28,30,39,37,33,40,42,43,34,36,38,29,31,41,32,35);(14,20)(17,23)(21,26)(24,27)(28,31,34,33)(29,35,37,43)(30,40,36,41)(32,38,42,39)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5024);