Finite Group DatabasebetaFinite Group Databasebeta| order | 3900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×#14519613 |
| Fitting, socle | C2×C52×C13 ⋊ C2×C3 |
| derived, Hall | C52×C13 ⋊ C22×C3 |
| Hall | C2×C5⋊D65 ⋊ C3 |
| Hall | C13×C52⋊C3 ⋊ C22 |
| Hall | C52⋊C3 ⋊ C2×D13 |
| Sylow | C52 ⋊ C2×C3×D13 |
| Sylow | C13 ⋊ C2×(C5⋊D5)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #14519613 |
| commutator, cosocle, hypocenter | C52×C13 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C13 | C2×C3 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 390 |
152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3900, 137);