Finite Group DatabasebetaFinite Group Databasebeta| order | 30044 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C37⋊(D29⋊C7) |
| unambiguous semidirect product | (C2×C37)⋊(D29⋊C7) |
| unambiguous semidirect product | (C2×C29⋊C7)⋊D37 |
| unambiguous semidirect product | (C2×D1073)⋊C7 |
| Fitting, socle | C2×C29×C37 ⋊ C2×C7 |
| derived, Hall | C29×C37 ⋊ C22×C7 |
| Hall | C37×C29⋊C7 ⋊ C22 |
| Hall | C2×D1073 ⋊ C7 |
| Hall | C29⋊C7 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D29⋊C7 |
| Sylow | C29 ⋊ C2×C7×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C37⋊(D29⋊C7) |
| commutator, cosocle, hypocenter | C29×C37 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C29×C37 | C2×C7 |
| LCS | G ▷ C29×C37 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2146 |
428 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30044, 22);