Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #29503071⋊C2 |
| unambiguous semidirect product | #29503075⋊C2 |
| unambiguous semidirect product | #29503077⋊C2 |
| Fitting, derived, Hall | C7×C361 ⋊ C22×C3 |
| Hall | D7×D361 ⋊ C3 |
| Hall | #21439055 ⋊ C22 |
| Sylow | C361 ⋊ C2×AGL(1,𝔽7) |
| Sylow | C7 ⋊ C2×D361⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C361 | C22×C3 |
| Frattini | C19 | #11716321⋊C2 |
| socle | C7×C19 | C2×D19⋊C3 |
| LCS | G ▷ C7×C361 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2527 |
Polycyclic presentation:
2^2,3,7,19^2|e^19=f^18,e^a=e^18f,f^a=f^18,d^b=d^6,d^c=d^4,e^c=e^11f^16,f^c=f^11314 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 28);