Finite Group DatabasebetaFinite Group Databasebeta| order | 25270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C5⋊(C7⋊(C19⋊D19)) |
| unambiguous semidirect product | C7⋊(C5⋊(C19⋊D19)) |
| unambiguous semidirect product | C19⋊D665 |
| Fitting, socle, derived, Hall | C5×C7×C192 ⋊ C2 |
| Hall | C7×C192 ⋊ D5 |
| Hall | C5×C192 ⋊ D7 |
| Sylow | C192 ⋊ D35 |
| Hall | C5×C7 ⋊ C19⋊D19 |
| Sylow | C7 ⋊ C5⋊(C19⋊D19) |
| Sylow | C5 ⋊ C7⋊(C19⋊D19) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C192 | C2 |
| LCS | G ▷ C5×C7×C192 | |
| UCS | C1 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12635 |
Polycyclic presentation:
2,5,7,19^2|b^a=b^4,c^a=c^6,d^a=d^18,e^a=e^186319 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25270, 26);