Finite Group DatabasebetaFinite Group Databasebeta| order | 33425 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C25 · Schur multiplier (H2) = C1 |
| direct product | C7×C191⋊C25 |
| unambiguous semidirect product | C191⋊(C7×C25) |
| unambiguous semidirect product | (C7×C191)⋊C25 |
| derived, Sylow | C191 ⋊ C7×C25 |
| Hall | C7×C191 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | C191⋊C5 |
| commutator, hypocenter | C191 | C7×C25 |
| Frattini | C5 | C7×C191⋊C5 |
| Fitting, socle, prime radical | C5×C7×C191 | C5 |
| cosocle | C5×C191 | C5×C7 |
| LCS | G ▷ C191 | |
| UCS | C1 ◁ C5×C7 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33425 |
1505 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33425, 2);