Finite Group DatabasebetaFinite Group Databasebeta| order | 34132 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D161⋊D53 |
| unambiguous semidirect product | D371⋊D23 |
| unambiguous semidirect product | D1219⋊D7 |
| Fitting, socle, derived, Hall | C7×C23×C53 ⋊ C22 |
| Hall | C23×C53 ⋊ C2×D7 |
| Hall | C7×C53 ⋊ C2×D23 |
| Hall | C7×C23 ⋊ C2×D53 |
| Sylow | C53 ⋊ D7×D23 |
| Sylow | C23 ⋊ D7×D53 |
| Sylow | C7 ⋊ D23×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C23×C53 | C22 |
| LCS | G ▷ C7×C23×C53 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8533 |
Polycyclic presentation:
2^2,7,23,53|d^a=d^22,e^a=e^52,c^b=c^6,d^b=d^222197 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34132, 20);