Finite Group DatabasebetaFinite Group Databasebeta| order | 16562 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C132 · Schur multiplier (H2) = C7×C13 |
| direct product | C132×C7⋊D7 |
| unambiguous semidirect product | C7⋊(C132×D7) |
| Fitting, socle, Hall | C72×C132 ⋊ C2 |
| derived, Sylow | C72 ⋊ C2×C132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C132 | C7⋊D7 |
| commutator, cosocle, hypocenter | C72 | C2×C132 |
| Frattini | C1 | G |
| Fitting, socle | C72×C132 | C2 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C132 | |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8281 |
4394 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C132×#5997, C13×#14579331, #45683902, … |
| maximal normal subgroup of | C132×#5997, C13×#14579331, #45683902, … |
| maximal quotient of | C132×C7⋊Dic7, C2×C132×C7⋊D7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16562, 29);