Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C361 · Schur multiplier (H2) = C1 |
| direct product | Dic21×C361 |
| unambiguous semidirect product | C3⋊(Dic7×C361) |
| unambiguous semidirect product | C7⋊(Dic3×C361) |
| derived, Hall | C3×C7 ⋊ C4×C361 |
| Hall | C3×C7×C361 ⋊ C4 |
| Hall | C7×C361 ⋊ Dic3 |
| Hall | C3×C361 ⋊ Dic7 |
| Sylow | C7 ⋊ Dic3×C361 |
| Sylow | C3 ⋊ Dic7×C361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C361 | D21 |
| commutator, hypocenter | C3×C7 | C4×C361 |
| Frattini | C2×C19 | C19×D21 |
| Fitting | C2×C3×C7×C361 | C2 |
| socle, prime radical, cosocle | C2×C3×C7×C19 | C2×C19 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C2×C361 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30324 |
8664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 23);