Finite Group DatabasebetaFinite Group Databasebeta| order | 30012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C41⋊(D61⋊C3) |
| unambiguous semidirect product | (C2×C41)⋊(D61⋊C3) |
| unambiguous semidirect product | (C2×C61⋊C3)⋊D41 |
| unambiguous semidirect product | (C2×D2501)⋊C3 |
| Fitting, socle | C2×C41×C61 ⋊ C2×C3 |
| derived, Hall | C41×C61 ⋊ C22×C3 |
| Hall | C2×D2501 ⋊ C3 |
| Hall | C41×C61⋊C3 ⋊ C22 |
| Hall | C61⋊C3 ⋊ C2×D41 |
| Sylow | C61 ⋊ C2×C3×D41 |
| Sylow | C41 ⋊ C2×D61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C41⋊(D61⋊C3) |
| commutator, cosocle, hypocenter | C41×C61 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C41×C61 | C2×C3 |
| LCS | G ▷ C41×C61 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5002 |
952 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30012, 22);