Finite Group DatabasebetaFinite Group Databasebeta| order | 6325 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C25 · Schur multiplier (H2) = C1 |
| direct product | C23×C11⋊C25 |
| unambiguous semidirect product | C11⋊(C23×C25) |
| unambiguous semidirect product | (C11×C23)⋊C25 |
| derived, Sylow | C11 ⋊ C23×C25 |
| Hall | C11×C23 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C23 | C11⋊C5 |
| commutator, hypocenter | C11 | C23×C25 |
| Frattini | C5 | C23×C11⋊C5 |
| Fitting, socle | C5×C11×C23 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C5×C23 | |
12 conjugacy classes of subgroups.
805 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×C11⋊C25, D23×C11⋊C25, C23×D11⋊C25, … |
| maximal normal subgroup of | C2×C23×C11⋊C25, D23×C11⋊C25, C23×D11⋊C25, … |
| maximal quotient of | C2×C23×C11⋊C25, C3×C23×C11⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6325, 3);