Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C43⋊#10596885 |
| Fitting, socle, Hall | C72×C43 ⋊ Dic3 |
| derived, Hall | C43×#3862 ⋊ C4 |
| Hall | #3862 ⋊ Dic43 |
| Sylow | C72 ⋊ Dic129 |
| Sylow | C43 ⋊ #10596885 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C43×#3862 | C4 |
| Fitting, socle | C72×C43 | Dic3 |
| prime radical, cosocle | C43×#64425 | C2 |
| LCS | G ▷ C43×#3862 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 602 |
Polycyclic presentation:
2^2,3,43,7^2|a^2=b,c^a=c^2,d^a=d^42,e^a=e^3f^4,f^a=ef^4,e^b=e^6,f^b=f^6,e^c=e^2f^6,f^c=f^4304 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 224);