Finite Group DatabasebetaFinite Group Databasebeta| order | 24660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C137 · Schur multiplier (H2) = C3 |
| direct product | C137×#4380 |
| Fitting, socle, Hall | C32×C5×C137 ⋊ C4 |
| derived, Hall | C32×C5 ⋊ C4×C137 |
| Hall | C32×C137 ⋊ AGL(1,𝔽5) |
| Hall | C5×C137 ⋊ #157 |
| Sylow | C32 ⋊ AGL(1,𝔽5)×C137 |
| Sylow | C5 ⋊ #157×C137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C137 | #4380 |
| commutator, hypocenter | C32×C5 | C4×C137 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C137 | C4 |
| prime radical | C3⋊D15×C137 | C2 |
| cosocle | C3⋊D15 | C2×C137 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C137 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4110 |
2055 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24660, 53);