Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52×C7 · Schur multiplier (H2) = C5 |
| direct product | C52×C7×Dic3 |
| unambiguous semidirect product | C3⋊(C4×C52×C7) |
| derived, Sylow | C3 ⋊ C4×C52×C7 |
| Hall | C3×C52×C7 ⋊ C4 |
| Hall | C3×C52 ⋊ C4×C7 |
| Hall | C3×C7 ⋊ C4×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52×C7 | D3 |
| commutator, hypocenter | C3 | C4×C52×C7 |
| Frattini | C2 | C52×D3×C7 |
| Fitting, socle, prime radical | C2×C3×C52×C7 | C2 |
| cosocle | C2×C3 | C2×C52×C7 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C52×C7 | |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 2100 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5)(11,12,13,14,15,16,17)(18,19)(20,21)(22,23,24);(6,7,8,9,10)(18,20,19,21)(23,24)1050 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×Dic3×C49, C52×C72×Dic3, C52×C7×Dic21, … |
| maximal normal subgroup of | C52×Dic3×C49, C52×C72×Dic3, C52×C7×C11×Dic3, … |
| maximal quotient of | C52×Dic3×C49, C52×C72×Dic3, C52×C7×Dic21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 63);