Finite Group DatabasebetaFinite Group Databasebeta| order | 16562 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C7 |
| direct product | C13×C7⋊D91 |
| unambiguous semidirect product | C7⋊(C13×D91) |
| unambiguous semidirect product | C13⋊(C13×C7⋊D7) |
| Fitting, socle, Hall | C72×C132 ⋊ C2 |
| derived | C72×C13 ⋊ C2×C13 |
| Sylow | C132 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C13×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C7⋊D91 |
| commutator, cosocle, hypocenter | C72×C13 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C72×C132 | C2 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C13 | |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1274 |
4160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×#14579330, #45683901, C13×D7×D91, … |
| maximal normal subgroup of | C13×#14579330, #45683901, C13×D7×D91, … |
| maximal quotient of | C13×C7⋊Dic91, C2×C13×C7⋊D91 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16562, 28);