Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, Hall | C52×C72 ⋊ C2×D3 |
| derived, Hall | C72×C52⋊C3 ⋊ C22 |
| Hall | C52⋊C3 ⋊ D72 |
| Sylow | C72 ⋊ #3874⋊C2 |
| Sylow | C52 ⋊ D7×D21 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C72×C52⋊C3 | C22 |
| Fitting, socle | C52×C72 | C2×D3 |
| LCS | G ▷ C72×C52⋊C3 | |
| UCS | C1 | |
156 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^2,3,7^2,5^2|c^a=c^2,d^a=d^6,e^a=e^6,g^a=f^4g^4,c^b=c^2,e^b=e^6,f^b=f^4,g^b=fg,f^c=g,g^c=f^4g^4182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 522);