Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of C3⋊(C7⋊#1042) |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C7⋊#1042) |
| unambiguous semidirect product | C7⋊(C3⋊#1042) |
| Fitting, socle, derived, Hall | C3×C52×C7 ⋊ C4 |
| Hall | C52×C7 ⋊ Dic3 |
| Hall | C3×C52 ⋊ Dic7 |
| Sylow | C52 ⋊ Dic21 |
| Hall | C3×C7 ⋊ #1042 |
| Sylow | C7 ⋊ C3⋊#1042 |
| Sylow | C3 ⋊ C7⋊#1042 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C7 | C4 |
| prime radical, cosocle | C3×C5×C7×D5 | C2 |
| LCS | G ▷ C3×C52×C7 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 420 |
Polycyclic presentation:
2^2,3,5^2,7|a^2=b,c^a=c^2,d^a=d^2,e^a=e^4,f^a=f^6,d^b=d^4213 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 134);