Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#11950 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #102 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C22×C11 | C2×#102 |
| prime radical | C23×C11 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
300 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,21,17,20,15,19)(14,22,23,27,24,18,25,26)(28,29,32,37,34,39,47,36,33,38,48,55,46,54,31,45)(30,40,42,51,44,53,58,57,43,56,59,35,49,50,41,52);(12,14)(13,18)(15,23)(16,25)(17,24)(19,26)(20,22)(21,27)(28,30,33,43)(29,35,38,51)(31,42,47,59)(32,41,48,58)(34,49,46,44)(36,53,45,50)(37,56,55,40)(39,57,54,52);(12,15,17,16)(13,19,20,21)(14,23,24,25)(18,26,22,27)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4938);