Finite Group DatabasebetaFinite Group Databasebeta| order | 17050 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25×C31 · Schur multiplier (H2) = C1 |
| direct product | C2×C31×C11⋊C25 |
| unambiguous semidirect product | (C2×C11)⋊(C25×C31) |
| derived, Sylow | C11 ⋊ C2×C25×C31 |
| Hall | C2×C11×C31 ⋊ C25 |
| Hall | C11×C31 ⋊ C2×C25 |
| Hall | C2×C11 ⋊ C25×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C31 | C11⋊C5 |
| commutator, hypocenter | C11 | C2×C25×C31 |
| Frattini | C5 | C2×C31×C11⋊C5 |
| Fitting, socle, prime radical | C2×C5×C11×C31 | C5 |
| cosocle | C5×C11 | C2×C5×C31 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C5×C31 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17050 |
2170 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C31×C11⋊C25, Dic31×C11⋊C25, C31×Dic11⋊C25, … |
| maximal normal subgroup of | C4×C31×C11⋊C25, Dic31×C11⋊C25, C31×Dic11⋊C25, … |
| maximal quotient of | C4×C31×C11⋊C25, C22×C31×C11⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17050, 3);