Finite Group DatabasebetaFinite Group Databasebeta| order | 25578 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C9⋊(D29⋊C7)) |
| unambiguous semidirect product | C9⋊(C7⋊(D29⋊C7)) |
| unambiguous semidirect product | (C29⋊C7)⋊D63 |
| unambiguous semidirect product | D1827⋊C7 |
| Fitting, derived | C7×C9×C29 ⋊ C2×C7 |
| Hall | C7×C9×C29⋊C7 ⋊ C2 |
| Hall | C7×C29⋊C7 ⋊ D9 |
| Hall | C9×C29 ⋊ C7×D7 |
| Sylow | C29 ⋊ C7×D63 |
| Sylow | C9 ⋊ C7⋊(D29⋊C7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C9×C29 | C2×C7 |
| Frattini | C3 | C3⋊(C7⋊(D29⋊C7)) |
| socle | C3×C7×C29 | D3×C7 |
| LCS | G ▷ C7×C9×C29 | |
| UCS | C1 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1827 |
Polycyclic presentation:
2,7,3,7,29,3|c^3=f^2,c^a=c^2f,d^a=d^6,e^a=e^28,f^a=f^2,e^b=e^16357 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25578, 53);