Finite Group DatabasebetaFinite Group Databasebeta| order | 2340 |
| isoclinism | isoclinic class of D45 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic45 |
| unambiguous semidirect product | C9⋊(C13×Dic5) |
| derived, Hall | C5×C9 ⋊ C4×C13 |
| Hall | C5×C9×C13 ⋊ C4 |
| Hall | C9×C13 ⋊ Dic5 |
| Hall | C5×C13 ⋊ Dic9 |
| Sylow | C9 ⋊ C13×Dic5 |
| Sylow | C5 ⋊ C13×Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D45 |
| commutator, hypocenter | C5×C9 | C4×C13 |
| Frattini | C2×C3 | C13×D15 |
| Fitting | C2×C5×C9×C13 | C2 |
| socle, prime radical | C2×C3×C5×C13 | D3 |
| cosocle | C2×C5×C9 | C2×C13 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C2×C13 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 2340 |
A minimal faithful permutation representation — 2 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,20,21,22,23,24,25,26)(27,28,29,30,31);(14,16,15,17)(19,26)(20,25)(21,24)(22,23)(28,31)(29,30)624 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×Dic225, C5×C13×Dic45, C13×C9⋊#1039, … |
| maximal normal subgroup of | C5×C13×Dic45, C7×C13×Dic45, C11×C13×Dic45, … |
| maximal quotient of | C13×Dic225, C5×C13×Dic45, C13×C9⋊#1039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2340, 11);