Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊Dic133 |
| derived, Hall | C7×C192 ⋊ C3×C4 |
| Hall | C7⋊(C19⋊Dic19) ⋊ C3 |
| Hall | C7×C19×C19⋊C3 ⋊ C4 |
| Hall | C19×C19⋊C3 ⋊ Dic7 |
| Sylow | C192 ⋊ C3×Dic7 |
| Sylow | C7 ⋊ (C19⋊C3)⋊Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C19⋊C3)⋊D133 |
| commutator, hypocenter | C7×C192 | C3×C4 |
| Fitting, socle, cosocle | C2×C7×C192 | C2×C3 |
| prime radical | C2×C7×C19×C19⋊C3 | C2 |
| LCS | G ▷ C7×C192 | |
| UCS | C1 ◁ C2 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1596 |
Polycyclic presentation:
2,3,7,19^2,2|a^2=f,c^a=c^6,d^a=d^18,e^a=e^18,d^b=d^71206 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 116);