Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of C3⋊(C7⋊#1035) |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C7⋊#1035) |
| unambiguous semidirect product | C7⋊(C3⋊#1035) |
| Fitting, derived, Hall | C3×C7×C25 ⋊ C4 |
| Hall | C7×C25 ⋊ Dic3 |
| Hall | C3×C25 ⋊ Dic7 |
| Sylow | C25 ⋊ Dic21 |
| Hall | C3×C7 ⋊ #1035 |
| Sylow | C7 ⋊ C3⋊#1035 |
| Sylow | C3 ⋊ C7⋊#1035 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C7×C25 | C4 |
| Frattini | C5 | C3⋊(C7⋊AGL(1,𝔽5)) |
| socle | C3×C5×C7 | AGL(1,𝔽5) |
| prime radical, cosocle | C3×C7×D25 | C2 |
| LCS | G ▷ C3×C7×C25 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 525 |
Polycyclic presentation:
2^2,3,5,7,5|a^2=b,d^5=f,c^a=c^2,d^a=d^2f,e^a=e^6,f^a=f^2,d^b=d^4f^4,f^b=f^4150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 23);