Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #11716321⋊D19 |
| Fitting, socle, derived, Hall | C7×C192 ⋊ C22×C3 |
| Hall | D19×D133 ⋊ C3 |
| Hall | C19×#87704 ⋊ C22 |
| Sylow | C192 ⋊ C2×AGL(1,𝔽7) |
| Sylow | C7 ⋊ D19×D19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C192 | C22×C3 |
| LCS | G ▷ C7×C192 | |
| UCS | C1 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 798 |
Polycyclic presentation:
2^2,3,7,19^2|d^a=d^6,e^a=e^18,f^b=f^18,d^c=d^2,f^c=f^7308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 157);