Finite Group DatabasebetaFinite Group Databasebeta| order | 24180 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #18012827⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C31 | C3×C4×C5 |
| prime radical | D13⋊C3×ΓL(1,𝔽32) | C2 |
| cosocle | D13×C31 | C2×C3×C5 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 403 |
Polycyclic presentation:
2,3,5,2,13,31|a^2=d,e^a=e^5,f^a=f^30,e^b=e^3,f^c=f^16,e^d=e^1289 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24180, 78);