Finite Group DatabasebetaFinite Group Databasebeta| order | 25074 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C3⋊(D199⋊C3) |
| unambiguous semidirect product | C3⋊(C7×D199⋊C3) |
| unambiguous semidirect product | (C199⋊C3)⋊(D3×C7) |
| unambiguous semidirect product | D597⋊(C3×C7) |
| Fitting, socle | C3×C7×C199 ⋊ C2×C3 |
| derived | C3×C199 ⋊ C2×C3×C7 |
| Hall | C3×C7×C199⋊C3 ⋊ C2 |
| Hall | C3×C199⋊C3 ⋊ C2×C7 |
| Hall | C7×C199 ⋊ C3×D3 |
| Sylow | C199 ⋊ C3×D3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊(D199⋊C3) |
| commutator, cosocle, hypocenter | C3×C199 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C199 | C2×C3 |
| LCS | G ▷ C3×C199 | |
| UCS | C1 ◁ C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4179 |
756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25074, 54);