Finite Group DatabasebetaFinite Group Databasebeta| order | 16562 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C13 |
| direct product | C7×C7⋊(C13⋊D13) |
| unambiguous semidirect product | C7⋊(C7×C13⋊D13) |
| unambiguous semidirect product | C13⋊(C7×D91) |
| Fitting, socle, Hall | C72×C132 ⋊ C2 |
| derived | C7×C132 ⋊ C2×C7 |
| Sylow | C132 ⋊ C7×D7 |
| Sylow | C72 ⋊ C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C7⋊(C13⋊D13) |
| commutator, cosocle, hypocenter | C7×C132 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C132 | C2 |
| LCS | G ▷ C7×C132 | |
| UCS | C1 ◁ C7 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2366 |
4151 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D13×D91, C7×D7×C13⋊D13, D91⋊D91, … |
| maximal normal subgroup of | C7×D13×D91, C7×D7×C13⋊D13, D91⋊D91, … |
| maximal quotient of | C7×C7⋊#10621725, C2×C7×C7⋊(C13⋊D13) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16562, 30);