Finite Group DatabasebetaFinite Group Databasebeta| order | 17325 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C25 · Schur multiplier (H2) = C1 |
| derived, Hall | C7×C11 ⋊ C9×C25 |
| Hall | C7×C11⋊C25 ⋊ C9 |
| Hall | C11×C7⋊C9 ⋊ C25 |
| Sylow | C11 ⋊ C25×C7⋊C9 |
| Sylow | C7 ⋊ C9×C11⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3×C5 | ΓL(1,𝔽8)×C11⋊C5 |
| commutator, hypocenter | C7×C11 | C9×C25 |
| Fitting, socle, prime radical, cosocle | C3×C5×C7×C11 | C3×C5 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C3×C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17325 |
525 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C7⋊C9×C11⋊C25, C7⋊C9×D11⋊C25, D7⋊C9×C11⋊C25, … |
| maximal normal subgroup of | C2×C7⋊C9×C11⋊C25, C7⋊C9×D11⋊C25, D7⋊C9×C11⋊C25, … |
| maximal quotient of | C2×C7⋊C9×C11⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17325, 2);