Finite Group DatabasebetaFinite Group Databasebeta| order | 7550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16836851⋊C2 |
| Fitting, socle, derived, Sylow | C151 ⋊ C2×C25 |
| Hall | #16836851 ⋊ C2 |
| Hall | D151 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C151 | C2×C25 |
| LCS | G ▷ C151 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^2,151|b^5=c,d^a=d^150,d^b=d^148,d^c=d^5953 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7550, 8);