Finite Group DatabasebetaFinite Group Databasebeta| order | 25578 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| Fitting, socle, derived | C3×C7×C29 ⋊ C2×C3×C7 |
| Hall | C3×ΓL(1,𝔽8)×C29⋊C7 ⋊ C2 |
| Hall | C7×C29⋊C7 ⋊ C3×D3 |
| Sylow | C29 ⋊ C7×C3⋊AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C29 | C2×C3×C7 |
| LCS | G ▷ C3×C7×C29 | |
| UCS | C1 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 609 |
Polycyclic presentation:
2,3,7,3,7,29|d^a=d^2,e^a=e^6,f^a=f^28,e^b=e^2,f^c=f^16114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25578, 93);