Finite Group DatabasebetaFinite Group Databasebeta| order | 23660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | ((C13⋊D13)⋊C7)⋊D5 |
| Fitting, socle, Hall | C5×C132 ⋊ C2×D7 |
| derived, Hall | C5×C132⋊C7 ⋊ C22 |
| Hall | C132⋊C7 ⋊ C2×D5 |
| Sylow | C132 ⋊ C2×D35 |
| Sylow | C5 ⋊ #14556975⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C132⋊C7 | C22 |
| Fitting, socle | C5×C132 | C2×D7 |
| LCS | G ▷ C5×C132⋊C7 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 455 |
Polycyclic presentation:
2^2,5,7,13^2|c^a=c^4,d^a=d^6,e^a=e^12f^7,e^b=e^12,f^b=f^12,e^d=e^8f^6,f^d=e^5f^1286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23660, 65);