Finite Group DatabasebetaFinite Group Databasebeta| order | 8125 |
| automorphism | ? |
| homology | Abelianization (H1) = C13 · Schur multiplier (H2) = C52 |
| unambiguous semidirect product | C54⋊C13 |
| Fitting, socle, derived, Sylow | C54 ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C54 | C13 |
| LCS | G ▷ C54 | |
| UCS | C1 | |
90 conjugacy classes of subgroups.
Polycyclic presentation:
13,5^4|b^a=b^3c^3d^3e,c^a=b^3c,d^a=b^3c^2d^2e^2,e^a=b^2c^4e^361 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8125, 16);