Finite Group DatabasebetaFinite Group Databasebeta| order | 21462 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C73 ⋊ C2×C3 |
| Hall | C73⋊#3862 ⋊ C2 |
| Hall | C7×D511 ⋊ C3 |
| Sylow | C73 ⋊ #64422 |
| Sylow | C72 ⋊ D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C73 | C2×C3 |
| LCS | G ▷ C72×C73 | |
| UCS | C1 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3066 |
Polycyclic presentation:
2,3,7^2,73|d^a=d^6,e^a=e^72,c^b=c^2,d^b=d^4,e^b=e^8605 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21462, 68);