Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C72×C25 ⋊ C3×C4 |
| Hall | C7⋊Dic175 ⋊ C3 |
| Hall | C25×#3861 ⋊ C4 |
| Hall | #3861 ⋊ Dic25 |
| Sylow | C72 ⋊ C3×Dic25 |
| Sylow | C25 ⋊ #10596874 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C25⋊#64424 |
| commutator, hypocenter | C72×C25 | C3×C4 |
| Frattini | C2×C5 | C5⋊#64424 |
| Fitting, cosocle | C2×C72×C25 | C2×C3 |
| socle | C2×C5×C72 | C3×D5 |
| prime radical | C2×C5×#3861 | D5 |
| LCS | G ▷ C72×C25 | |
| UCS | C1 ◁ C2 | |
180 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,7^2,2,5|a^2=f,c^5=g^4,c^a=c^4g,d^a=d^6,e^a=e^6,g^a=g^4,d^b=d^2,e^b=e^2484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 81);