Finite Group DatabasebetaFinite Group Databasebeta| order | 28340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#19150873 |
| Fitting, socle, Hall | C5×C13×C109 ⋊ C4 |
| derived, Hall | C13×C109 ⋊ C4×C5 |
| Hall | C5×C109 ⋊ Dic13 |
| Sylow | C109 ⋊ C5×Dic13 |
| Hall | C5×C13 ⋊ #89137 |
| Sylow | C13 ⋊ C5×#89137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #19150873 |
| commutator, hypocenter | C13×C109 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C109 | C4 |
| prime radical | C5×C13×D109 | C2 |
| cosocle | C13×D109 | C2×C5 |
| LCS | G ▷ C13×C109 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7085 |
1835 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28340, 15);