Finite Group DatabasebetaFinite Group Databasebeta| order | 16562 |
| isoclinism | isoclinic class of C13⋊D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7×C13 |
| direct product | C72×C13⋊D13 |
| unambiguous semidirect product | C13⋊(C72×D13) |
| Fitting, socle, Hall | C72×C132 ⋊ C2 |
| derived, Sylow | C132 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | C13⋊D13 |
| commutator, cosocle, hypocenter | C132 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C132 | C2 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C72 | |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8281 |
4214 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×D132, C72×#10621729, C72×#10621728, … |
| maximal normal subgroup of | C72×D132, C72×#10621729, C72×#10621728, … |
| maximal quotient of | C72×#10621725, C2×C72×C13⋊D13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16562, 33);