Finite Group DatabasebetaFinite Group Databasebeta| order | 34132 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C23⋊#6157) |
| unambiguous semidirect product | C23⋊(C7⋊#6157) |
| Fitting, socle, derived, Hall | C7×C23×C53 ⋊ C4 |
| Hall | C23×C53 ⋊ Dic7 |
| Hall | C7×C53 ⋊ Dic23 |
| Hall | C7×C23 ⋊ #6157 |
| Sylow | C53 ⋊ Dic161 |
| Sylow | C23 ⋊ C7⋊#6157 |
| Sylow | C7 ⋊ C23⋊#6157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C23×C53 | C4 |
| prime radical, cosocle | C7×C23×D53 | C2 |
| LCS | G ▷ C7×C23×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8533 |
Polycyclic presentation:
2^2,7,23,53|a^2=b,c^a=c^6,d^a=d^22,e^a=e^30,e^b=e^522257 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34132, 15);