Finite Group DatabasebetaFinite Group Databasebeta| order | 1375 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C25 · Schur multiplier (H2) = C5 |
| direct product | C5×C11⋊C25 |
| unambiguous semidirect product | (C5×C11)⋊C25 |
| derived, Sylow | C11 ⋊ C5×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C11⋊C5 |
| commutator, hypocenter | C11 | C5×C25 |
| Frattini | C5 | C5×C11⋊C5 |
| Fitting, socle, prime radical | C52×C11 | C5 |
| cosocle | C5×C11 | C52 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C52 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1375 |
175 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1375, 8);