Finite Group DatabasebetaFinite Group Databasebeta| order | 14555 |
| isoclinism | isoclinic class of C71⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×C71⋊C5 |
| unambiguous semidirect product | C71⋊(C5×C41) |
| Fitting, socle, Hall | C41×C71 ⋊ C5 |
| derived, Sylow | C71 ⋊ C5×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | C71⋊C5 |
| commutator, cosocle, hypocenter | C71 | C5×C41 |
| Frattini | C1 | G |
| Fitting, socle | C41×C71 | C5 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C41 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2911 |
779 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C41×C71⋊C5, C41×D71⋊C5, D41×C71⋊C5, … |
| maximal normal subgroup of | C2×C41×C71⋊C5, C41×D71⋊C5, D41×C71⋊C5, … |
| maximal quotient of | C2×C41×C71⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14555, 2);