Finite Group DatabasebetaFinite Group Databasebeta| order | 25578 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3 |
| Fitting, socle | C2×C3×C7×C29 ⋊ C3×C7 |
| derived | C7×C29 ⋊ C2×C32×C7 |
| Hall | C2×C7×C29⋊C7 ⋊ C32 |
| Hall | C7×C29⋊C7 ⋊ C2×C32 |
| Hall | C2×C29 ⋊ C3×C7×ΓL(1,𝔽8) |
| Sylow | C29 ⋊ C2×C3×C7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | ΓL(1,𝔽8)×C29⋊C7 |
| commutator, cosocle, hypocenter | C7×C29 | C2×C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C29 | C3×C7 |
| LCS | G ▷ C7×C29 | |
| UCS | C1 ◁ C2×C3 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1218 |
330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25578, 97);