Finite Group DatabasebetaFinite Group Databasebeta| order | 17395 |
| isoclinism | isoclinic class of C71⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×C71⋊C5 |
| unambiguous semidirect product | (C49×C71)⋊C5 |
| Fitting, Hall | C49×C71 ⋊ C5 |
| derived, Sylow | C71 ⋊ C5×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | C71⋊C5 |
| commutator, hypocenter | C71 | C5×C49 |
| Frattini | C7 | C7×C71⋊C5 |
| Fitting | C49×C71 | C5 |
| socle, cosocle | C7×C71 | C5×C7 |
| prime radical | C7×C71⋊C5 | C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C49 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3479 |
931 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C49×C71⋊C5, C49×D71⋊C5, D49×C71⋊C5, … |
| maximal normal subgroup of | C2×C49×C71⋊C5, C49×D71⋊C5, D49×C71⋊C5, … |
| maximal quotient of | C2×C49×C71⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17395, 4);