Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of ((C5⋊D5)⋊C3)⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | ((C5⋊D5)⋊C3)⋊D7 |
| Fitting, socle, Hall | C52×C7 ⋊ C2×D3 |
| derived, Hall | C7×C52⋊C3 ⋊ C22 |
| Hall | C52⋊C3 ⋊ C2×D7 |
| Sylow | C52 ⋊ C2×D21 |
| Sylow | C7 ⋊ #3874⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C7×C52⋊C3 | C22 |
| Fitting, socle | C52×C7 | C2×D3 |
| LCS | G ▷ C7×C52⋊C3 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 105 |
Polycyclic presentation:
2^2,3,7,5^2|c^a=c^2,d^a=d^6,e^a=e^4f^4,e^b=e^4,f^b=f^4,e^c=f,f^c=e^4f^444 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 85);