Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of D35⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D35⋊D15 |
| Fitting, socle, derived, Hall | C3×C52×C7 ⋊ C22 |
| Hall | C52×C7 ⋊ C2×D3 |
| Hall | C3×C52 ⋊ C2×D7 |
| Sylow | C52 ⋊ D3×D7 |
| Hall | C3×C7 ⋊ D52 |
| Sylow | C7 ⋊ D5×D15 |
| Sylow | C3 ⋊ (C5⋊D5)⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C7 | C22 |
| LCS | G ▷ C3×C52×C7 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 210 |
Polycyclic presentation:
2^2,3,5^2,7|d^a=d^4,f^a=f^6,c^b=c^2,d^b=d^4,e^b=e^4153 conjugacy classes — view the full character table.
| maximal subgroup of | D245⋊D15, C7×D35⋊D15, #28413548, … |
| maximal normal subgroup of | C7×D35⋊D15, C11×D35⋊D15, C13×D35⋊D15, … |
| maximal quotient of | D245⋊D15, C7×D35⋊D15, #28413548, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 143);