Finite Group DatabasebetaFinite Group Databasebeta| order | 17391 |
| isoclinism | isoclinic class of C31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11×C17 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C11×C17×C31 ⋊ C3 |
| derived, Sylow | C31 ⋊ C3×C11×C17 |
| Hall | C17×C31 ⋊ C3×C11 |
| Hall | C11×C31 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C17 | C31⋊C3 |
| commutator, cosocle, hypocenter | C31 | C3×C11×C17 |
| Frattini | C1 | G |
| Fitting, socle | C11×C17×C31 | C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C11×C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5797 |
2431 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11×C17×C31⋊C3, C11×C17×D31⋊C3, C11×D17×C31⋊C3, … |
| maximal normal subgroup of | C2×C11×C17×C31⋊C3, C11×C17×D31⋊C3, C11×D17×C31⋊C3, … |
| maximal quotient of | C2×C11×C17×C31⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17391, 2);