Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C3⋊(C7⋊(C19⋊Dic19)) |
| unambiguous semidirect product | C7⋊(C3⋊(C19⋊Dic19)) |
| unambiguous semidirect product | C19⋊Dic399 |
| derived, Hall | C3×C7×C192 ⋊ C4 |
| Hall | C7×C192 ⋊ Dic3 |
| Hall | C3×C192 ⋊ Dic7 |
| Sylow | C192 ⋊ Dic21 |
| Hall | C3×C7 ⋊ C19⋊Dic19 |
| Sylow | C7 ⋊ C3⋊(C19⋊Dic19) |
| Sylow | C3 ⋊ C7⋊(C19⋊Dic19) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C7⋊(C19⋊D19)) |
| commutator, hypocenter | C3×C7×C192 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C7×C192 | C2 |
| LCS | G ▷ C3×C7×C192 | |
| UCS | C1 ◁ C2 | |
264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30324 |
Polycyclic presentation:
2,3,7,19^2,2|a^2=f,b^a=b^2,c^a=c^6,d^a=d^18,e^a=e^187584 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 130);