Finite Group DatabasebetaFinite Group Databasebeta| order | 16562 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C132⋊C49 ⋊ C2 |
| Sylow | C132 ⋊ D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C132⋊C49 | C2 |
| Frattini | C7 | #14556975 |
| Fitting, socle | C7×C132 | D7 |
| LCS | G ▷ C132⋊C49 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 637 |
Polycyclic presentation:
2,7,13^2,7|b^7=e^6,b^a=b^6e,d^a=cd^12,e^a=e^6,c^b=cd^6,d^b=cd^7128 conjugacy classes — view the full character table.
| maximal subgroup of | #30658555⋊C2, C2×#30658555 |
| maximal normal subgroup of | #30658555⋊C2, C2×#30658555 |
| maximal quotient of | #45683817, C2×#30658555 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16562, 12);