Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×Dic21 |
| unambiguous semidirect product | C3⋊(C25×Dic7) |
| unambiguous semidirect product | C7⋊(Dic3×C25) |
| derived, Hall | C3×C7 ⋊ C4×C25 |
| Hall | C3×C7×C25 ⋊ C4 |
| Hall | C7×C25 ⋊ Dic3 |
| Hall | C3×C25 ⋊ Dic7 |
| Sylow | C7 ⋊ Dic3×C25 |
| Sylow | C3 ⋊ C25×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C25 | D21 |
| commutator, hypocenter | C3×C7 | C4×C25 |
| Frattini | C2×C5 | C5×D21 |
| Fitting | C2×C3×C7×C25 | C2 |
| socle, prime radical, cosocle | C2×C3×C5×C7 | C2×C5 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C2×C25 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2100 |
A minimal faithful permutation representation — 2 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25)(26,27)(28,29)(30,31,32)(33,34,35,36,37,38,39);(26,28,27,29)(31,32)(34,39)(35,38)(36,37)600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×Dic147, C7×C25×Dic21, C25×C3⋊(C7⋊Dic7), … |
| maximal normal subgroup of | C7×C25×Dic21, C11×C25×Dic21, C13×C25×Dic21, … |
| maximal quotient of | C25×Dic147, C7×C25×Dic21, C25×C3⋊(C7⋊Dic7), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 10);