Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C192 · Schur multiplier (H2) = C19 |
| direct product | C192×Dic21 |
| unambiguous semidirect product | C3⋊(C192×Dic7) |
| unambiguous semidirect product | C7⋊(Dic3×C192) |
| derived, Hall | C3×C7 ⋊ C4×C192 |
| Hall | C3×C7×C192 ⋊ C4 |
| Hall | C7×C192 ⋊ Dic3 |
| Hall | C3×C192 ⋊ Dic7 |
| Sylow | C7 ⋊ Dic3×C192 |
| Sylow | C3 ⋊ C192×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C192 | D21 |
| commutator, hypocenter | C3×C7 | C4×C192 |
| Frattini | C2 | C192×D21 |
| Fitting, socle, prime radical | C2×C3×C7×C192 | C2 |
| cosocle | C2×C3×C7 | C2×C192 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C2×C192 | |
264 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, 132);