Finite Group DatabasebetaFinite Group Databasebeta| order | 24850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×D5×C71⋊C7 |
| unambiguous semidirect product | C5⋊(C2×C5×C71⋊C7) |
| unambiguous semidirect product | (C5×D5×C71)⋊C7 |
| Fitting, socle, Hall | C52×C71 ⋊ C2×C7 |
| derived | C5×C71 ⋊ C2×C5×C7 |
| Hall | C52×C71⋊C7 ⋊ C2 |
| Hall | C5×D5×C71 ⋊ C7 |
| Sylow | C71 ⋊ C5×C7×D5 |
| Sylow | C52 ⋊ C2×C71⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×C71⋊C7 |
| commutator, cosocle, hypocenter | C5×C71 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C71 | C2×C7 |
| LCS | G ▷ C5×C71 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 710 |
340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24850, 26);