Finite Group DatabasebetaFinite Group Databasebeta| order | 17325 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7×C25 · Schur multiplier (H2) = C3 |
| derived, Sylow | C11 ⋊ C32×C7×C25 |
| Hall | C32×C7×C11 ⋊ C25 |
| Hall | C32×C11 ⋊ C7×C25 |
| Hall | C7×C11 ⋊ C32×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5×C7 | C11⋊C5 |
| commutator, hypocenter | C11 | C32×C7×C25 |
| Frattini | C5 | C32×C7×C11⋊C5 |
| Fitting, socle, prime radical | C32×C5×C7×C11 | C5 |
| cosocle | C5×C11 | C32×C5×C7 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C32×C5×C7 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17325 |
2205 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C7×D11⋊C25, C32×C7⋊(D11⋊C25), C32×D7×C11⋊C25, … |
| maximal normal subgroup of | C32×C7×D11⋊C25, C32×C7⋊(D11⋊C25), C32×D7×C11⋊C25, … |
| maximal quotient of | C2×C32×C7×C11⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17325, 7);