Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C19 |
| direct product | C2×C3⋊(C7⋊(C19⋊D19)) |
| unambiguous semidirect product | (C2×C3)⋊(C7⋊(C19⋊D19)) |
| unambiguous semidirect product | (C2×C7)⋊(C3⋊(C19⋊D19)) |
| unambiguous semidirect product | (C2×C19)⋊D399 |
| Fitting, socle | C2×C3×C7×C192 ⋊ C2 |
| derived, Hall | C3×C7×C192 ⋊ C22 |
| Hall | C7×C192 ⋊ C2×D3 |
| Hall | C3×C192 ⋊ C2×D7 |
| Sylow | C192 ⋊ C2×D21 |
| Hall | C3×C7 ⋊ C2×C19⋊D19 |
| Sylow | C7 ⋊ C2×C3⋊(C19⋊D19) |
| Sylow | C3 ⋊ C2×C7⋊(C19⋊D19) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(C7⋊(C19⋊D19)) |
| commutator, cosocle, hypocenter | C3×C7×C192 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C192 | C2 |
| LCS | G ▷ C3×C7×C192 | |
| UCS | C1 ◁ C2 | |
440 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15162 |
7584 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 320);