Finite Group DatabasebetaFinite Group Databasebeta| order | 30084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | D3×C23×D109 |
| unambiguous semidirect product | (D3×C109)⋊(C2×C23) |
| unambiguous semidirect product | (C3×D109)⋊(C2×C23) |
| unambiguous semidirect product | D327⋊(C2×C23) |
| Fitting, socle, Hall | C3×C23×C109 ⋊ C22 |
| derived, Hall | C3×C109 ⋊ C22×C23 |
| Hall | C23×C109 ⋊ C2×D3 |
| Sylow | C109 ⋊ C2×D3×C23 |
| Hall | C3×C23 ⋊ C2×D109 |
| Sylow | C3 ⋊ C2×C23×D109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×D109 |
| commutator, cosocle, hypocenter | C3×C109 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C109 | C22 |
| LCS | G ▷ C3×C109 | |
| UCS | C1 ◁ C23 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7521 |
3864 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30084, 24);