Finite Group DatabasebetaFinite Group Databasebeta| order | 25116 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10587717⋊D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13×C23 | C22×C3 |
| LCS | G ▷ C7×C13×C23 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2093 |
Polycyclic presentation:
2^2,3,7,13,23|d^a=d^6,f^a=f^22,e^b=e^12,d^c=d^2,e^c=e^9288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25116, 65);