Finite Group DatabasebetaFinite Group Databasebeta| order | 25620 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C61 | C3×C4 |
| prime radical | D5×#13046197 | C2 |
| cosocle | C7×D5×C61 | C2×C3 |
| LCS | G ▷ C5×C7×C61 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2135 |
Polycyclic presentation:
2,3,2,5,7,61|a^2=c,d^a=d^2,e^a=e^6,e^b=e^2,f^b=f^47,d^c=d^4359 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25620, 144);