Finite Group DatabasebetaFinite Group Databasebeta| order | 25270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#16813380 |
| Fitting, socle, Hall | C7×C192 ⋊ D5 |
| derived, Hall | C7×C192⋊C5 ⋊ C2 |
| Hall | C192⋊C5 ⋊ D7 |
| Sylow | C192 ⋊ D35 |
| Sylow | C7 ⋊ #16813380 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C7×C192⋊C5 | C2 |
| Fitting, socle | C7×C192 | D5 |
| LCS | G ▷ C7×C192⋊C5 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 665 |
Polycyclic presentation:
2,5,7,19^2|b^a=b^4,c^a=c^6,d^a=de,e^a=e^18,d^b=d^5e^11,e^b=d^4e^9298 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25270, 13);