Finite Group DatabasebetaFinite Group Databasebeta| order | 21350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(D61⋊C25) |
| unambiguous semidirect product | D427⋊C25 |
| unambiguous semidirect product | (C61⋊C25)⋊D7 |
| derived, Hall | C7×C61 ⋊ C2×C25 |
| Hall | C7×C61⋊C25 ⋊ C2 |
| Hall | C61⋊C25 ⋊ D7 |
| Hall | D427 ⋊ C25 |
| Sylow | C61 ⋊ D7×C25 |
| Sylow | C7 ⋊ D61⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C7⋊(D61⋊C5) |
| commutator, hypocenter | C7×C61 | C2×C25 |
| Fitting, socle, cosocle | C5×C7×C61 | C2×C5 |
| prime radical | C5×D427 | C5 |
| LCS | G ▷ C7×C61 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10675 |
Polycyclic presentation:
2,5,7,61,5|b^5=e,c^a=c^6,d^a=d^60,d^b=d^9335 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21350, 12);