Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C3⋊(C7⋊Dic175) |
| unambiguous semidirect product | C7⋊Dic525 |
| derived, Hall | C3×C72×C25 ⋊ C4 |
| Hall | C72×C25 ⋊ Dic3 |
| Hall | C3×C72 ⋊ Dic25 |
| Hall | C3×C25 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ Dic75 |
| Sylow | C25 ⋊ C3⋊(C7⋊Dic7) |
| Sylow | C3 ⋊ C7⋊Dic175 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(C7⋊D175) |
| commutator, hypocenter | C3×C72×C25 | C4 |
| Frattini | C2×C5 | C3⋊(C5⋊(C7⋊D7)) |
| Fitting, cosocle | C2×C3×C72×C25 | C2 |
| socle, prime radical | C2×C3×C5×C72 | D5 |
| LCS | G ▷ C3×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,b^a=b^2,c^a=c^4g,d^a=d^6,e^a=e^6,g^a=g^43678 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 102);