Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of D7⋊((C5⋊D5)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | D7⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | (D7⋊(C52⋊C3))⋊C2 |
| unambiguous semidirect product | ((C5⋊D5)⋊ΓL(1,𝔽8))⋊C2 |
| unambiguous semidirect product | #11760386⋊C2 |
| Fitting, socle, derived, Hall | C52×C7 ⋊ C22×C3 |
| Hall | D7×C5⋊D5 ⋊ C3 |
| Hall | C7⋊(C52⋊C3) ⋊ C22 |
| Sylow | C52 ⋊ C2×AGL(1,𝔽7) |
| Sylow | C7 ⋊ C2×(C5⋊D5)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7 | C22×C3 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 105 |
Polycyclic presentation:
2^2,3,5^2,7|f^a=f^6,d^b=d^4,e^b=e^4,d^c=de^3,e^c=d^4e^3,f^c=f^234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 93);