Finite Group DatabasebetaFinite Group Databasebeta| order | 3900 |
| isoclinism | isoclinic class of C22⋊(C13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C2×C5 |
| Fitting, socle, Hall | C22×C52×C13 ⋊ C3 |
| derived, Hall | C22×C13 ⋊ C3×C52 |
| Hall | C52×C13 ⋊ A4 |
| Hall | C22×C52 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ C52×A4 |
| Sylow | C22 ⋊ C52×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C22⋊(C13⋊C3) |
| commutator, cosocle, hypocenter | C22×C13 | C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C22×C52×C13 | C3 |
| LCS | G ▷ C22×C13 | |
| UCS | C1 ◁ C52 | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 1300 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3,4,5)(12,13,14)(16,17,19)(18,21,24)(20,23,22)(25,27,26);(6,7,8,9,10)(11,14)(12,13)(15,16,18,17,20,24,21,25,27,19,22,26,23)500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3900, 203);