Finite Group DatabasebetaFinite Group Databasebeta| order | 16562 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#14556975 |
| Fitting, socle | C7×C132 ⋊ D7 |
| derived | C132⋊C7 ⋊ C2×C7 |
| Hall | C7×C132⋊C7 ⋊ C2 |
| Sylow | C132 ⋊ C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #14556975 |
| commutator, cosocle, hypocenter | C132⋊C7 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C132 | D7 |
| LCS | G ▷ C132⋊C7 | |
| UCS | C1 ◁ C7 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 637 |
245 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14556975⋊C2, D7×#14556975, #14556975⋊D7, … |
| maximal normal subgroup of | C7×#14556975⋊C2, D7×#14556975, #14556975⋊D7, … |
| maximal quotient of | C7×#17990042, C2×C7×#14556975 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16562, 21);