Finite Group DatabasebetaFinite Group Databasebeta| order | 24620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic1231⋊C5 |
| unambiguous semidirect product | (C1231⋊C5)⋊C4 |
| derived, Sylow | C1231 ⋊ C4×C5 |
| Hall | C1231⋊C5 ⋊ C4 |
| Hall | Dic1231 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1231⋊C5 |
| commutator, hypocenter | C1231 | C4×C5 |
| Fitting, socle, cosocle | C2×C1231 | C2×C5 |
| prime radical | C2×C1231⋊C5 | C2 |
| LCS | G ▷ C1231 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4924 |
Polycyclic presentation:
2,5,1231,2|a^2=d,c^a=c^1230,c^b=c^401266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24620, 2);