Finite Group DatabasebetaFinite Group Databasebeta| order | 24180 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #18012812⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #14559023⋊C5 |
| commutator, hypocenter | C13×C31 | C3×C4×C5 |
| Fitting, socle, cosocle | C2×C13×C31 | C2×C3×C5 |
| prime radical | C2×#11925881⋊C5 | C2 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1612 |
Polycyclic presentation:
2,3,5,13,31,2|a^2=f,e^a=e^30,d^b=d^3,e^b=e^5,e^c=e^16166 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24180, 64);