Finite Group DatabasebetaFinite Group Databasebeta| order | 23660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C169 · Schur multiplier (H2) = C1 |
| direct product | Dic35×C169 |
| unambiguous semidirect product | C7⋊(Dic5×C169) |
| derived, Hall | C5×C7 ⋊ C4×C169 |
| Hall | C5×C7×C169 ⋊ C4 |
| Hall | C7×C169 ⋊ Dic5 |
| Hall | C5×C169 ⋊ Dic7 |
| Sylow | C7 ⋊ Dic5×C169 |
| Sylow | C5 ⋊ Dic7×C169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C169 | D35 |
| commutator, hypocenter | C5×C7 | C4×C169 |
| Frattini | C2×C13 | C13×D35 |
| Fitting | C2×C5×C7×C169 | C2 |
| socle, prime radical, cosocle | C2×C5×C7×C13 | C2×C13 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C2×C169 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23660 |
6422 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23660, 7);