Finite Group DatabasebetaFinite Group Databasebeta| order | 18724 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×Dic151 |
| unambiguous semidirect product | C151⋊(C4×C31) |
| derived, Sylow | C151 ⋊ C4×C31 |
| Hall | C31×C151 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | D151 |
| commutator, hypocenter | C151 | C4×C31 |
| Frattini | C2 | C31×D151 |
| Fitting, socle, prime radical | C2×C31×C151 | C2 |
| cosocle | C2×C151 | C2×C31 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C2×C31 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18724 |
4774 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18724, 3);