Finite Group DatabasebetaFinite Group Databasebeta| order | 25578 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×D21×C29⋊C7 |
| unambiguous semidirect product | C3⋊(C3×D7×C29⋊C7) |
| unambiguous semidirect product | (C3×C29×D21)⋊C7 |
| Fitting, socle | C32×C7×C29 ⋊ C2×C7 |
| derived | C3×C7×C29 ⋊ C2×C3×C7 |
| Hall | C32×C7×C29⋊C7 ⋊ C2 |
| Hall | C7×C29⋊C7 ⋊ C3×D3 |
| Hall | C32×C29 ⋊ C7×D7 |
| Sylow | C29 ⋊ C3×C7×D21 |
| Sylow | C32 ⋊ D7×C29⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D21×C29⋊C7 |
| commutator, cosocle, hypocenter | C3×C7×C29 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C29 | C2×C7 |
| LCS | G ▷ C3×C7×C29 | |
| UCS | C1 ◁ C3 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1218 |
396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25578, 111);