Finite Group DatabasebetaFinite Group Databasebeta| order | 25652 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊(C11⋊#6157) |
| Fitting, socle, derived, Hall | C112×C53 ⋊ C4 |
| Sylow | C112 ⋊ #6157 |
| Sylow | C53 ⋊ C11⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112×C53 | C4 |
| prime radical, cosocle | C112×D53 | C2 |
| LCS | G ▷ C112×C53 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6413 |
Polycyclic presentation:
2^2,11^2,53|a^2=b,c^a=c^10,d^a=d^10,e^a=e^30,e^b=e^521697 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25652, 28);