Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of C22⋊(C7⋊(C52⋊C3)) |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | C22⋊(C7⋊(C52⋊C3)) |
| unambiguous semidirect product | C7⋊(C22⋊(C52⋊C3)) |
| unambiguous semidirect product | C52⋊(C22⋊ΓL(1,𝔽8)) |
| Fitting, socle, derived, Hall | C22×C52×C7 ⋊ C3 |
| Hall | C52×C7 ⋊ A4 |
| Hall | C22×C52 ⋊ ΓL(1,𝔽8) |
| Hall | C22×C7 ⋊ C52⋊C3 |
| Sylow | C52 ⋊ C22⋊ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C22⋊(C52⋊C3) |
| Sylow | C22 ⋊ C7⋊(C52⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C52×C7 | C3 |
| LCS | G ▷ C22×C52×C7 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 210 |
Polycyclic presentation:
3,2^2,5^2,7|b^a=c,c^a=bc,d^a=de^2,e^a=de^3,f^a=f^2236 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 153);