Finite Group DatabasebetaFinite Group Databasebeta| order | 16562 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C13 |
| direct product | C2×C132⋊C49 |
| unambiguous semidirect product | (C2×C132)⋊C49 |
| derived, Sylow | C132 ⋊ C2×C49 |
| Hall | C2×C132 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | C132⋊C7 |
| commutator, hypocenter | C132 | C2×C49 |
| Frattini | C7 | C2×C132⋊C7 |
| Fitting, socle, prime radical | C2×C7×C132 | C7 |
| cosocle | C7×C132 | C2×C7 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C2×C7 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1274 |
434 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45683817, #10621725⋊C49, C4×C132⋊C49, … |
| maximal normal subgroup of | #45683817, #10621725⋊C49, C4×C132⋊C49, … |
| maximal quotient of | C4×C132⋊C49, C22×C132⋊C49 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16562, 14);