Finite Group DatabasebetaFinite Group Databasebeta| order | 16562 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C169 · Schur multiplier (H2) = C7 |
| direct product | C7⋊D7×C169 |
| unambiguous semidirect product | C7⋊(D7×C169) |
| Fitting, Hall | C72×C169 ⋊ C2 |
| derived, Sylow | C72 ⋊ C2×C169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C169 | C7⋊D7 |
| commutator, hypocenter | C72 | C2×C169 |
| Frattini | C13 | C13×C7⋊D7 |
| Fitting | C72×C169 | C2 |
| socle, cosocle | C72×C13 | C2×C13 |
| prime radical | C13×C7⋊D7 | C13 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C169 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8281 |
4394 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7⋊D7×D169, D72×C169, (C7⋊D7)⋊D169, … |
| maximal normal subgroup of | C7⋊D7×D169, D72×C169, (C7⋊D7)⋊D169, … |
| maximal quotient of | C169×C7⋊Dic7, C2×C7⋊D7×C169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16562, 9);