Finite Group DatabasebetaFinite Group Databasebeta| order | 3900 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| direct product | C3×#13049937 |
| Fitting, socle, Hall | C3×C52×C13 ⋊ C4 |
| derived, Hall | C52×C13 ⋊ C3×C4 |
| Hall | C3×C52 ⋊ #261 |
| Hall | C3×C13 ⋊ #1039 |
| Sylow | C52 ⋊ C3×#261 |
| Sylow | C13 ⋊ C3×#1039 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #13049937 |
| commutator, hypocenter | C52×C13 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C13 | C4 |
| prime radical | C3×C52×D13 | C2 |
| cosocle | C52×D13 | C2×C3 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 975 |
309 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26043366, #26043387, #26043389, … |
| maximal normal subgroup of | #26043366, #26043387, #26043389, … |
| maximal quotient of | C9×#13049937, C32×#13049937, C3×C3⋊#13049937, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3900, 158);