Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of C7⋊#3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#64470 |
| derived, Hall | C7×C52⋊C3 ⋊ C4 |
| Hall | C52×C7 ⋊ Dic3 |
| Hall | C52⋊C3 ⋊ Dic7 |
| Sylow | C52 ⋊ Dic21 |
| Sylow | C7 ⋊ #64470 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊#3874 |
| commutator, hypocenter | C7×C52⋊C3 | C4 |
| Fitting, socle | C2×C52×C7 | D3 |
| prime radical, cosocle | C2×C7×C52⋊C3 | C2 |
| LCS | G ▷ C7×C52⋊C3 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 420 |
Polycyclic presentation:
2,3,7,5^2,2|a^2=f,b^a=b^2,c^a=c^6,d^a=d^2e,e^a=d^2e^3,d^b=d^2e^4,e^b=d^2e^292 conjugacy classes — view the full character table.
| maximal subgroup of | C49⋊#64470, C7×C7⋊#64470, C7⋊(C7⋊#64470), … |
| maximal normal subgroup of | C7×C7⋊#64470, C11×C7⋊#64470, C13×C7⋊#64470, … |
| maximal quotient of | C49⋊#64470, C7×C7⋊#64470, C7⋊(C7⋊#64470), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 43);