Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, derived, Hall | C3×C52×C72 ⋊ C22 |
| Hall | C52×C72 ⋊ C2×D3 |
| Hall | C3×C72 ⋊ D52 |
| Hall | C3×C52 ⋊ D72 |
| Sylow | C72 ⋊ D15⋊D5 |
| Sylow | C52 ⋊ D21⋊D7 |
| Sylow | C3 ⋊ D352 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C72 | C22 |
| LCS | G ▷ C3×C52×C72 | |
| UCS | C1 | |
288 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^2,3,5^2,7^2|c^a=c^2,d^a=d^4,f^a=f^6,d^b=d^4,e^b=e^4,f^b=f^6,g^b=g^6975 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 737);