Finite Group DatabasebetaFinite Group Databasebeta| order | 13900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D5×D139 |
| unambiguous semidirect product | (D5×C139)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D139)⋊(C2×C5) |
| unambiguous semidirect product | D695⋊(C2×C5) |
| Fitting, socle, Hall | C52×C139 ⋊ C22 |
| derived | C5×C139 ⋊ C22×C5 |
| Sylow | C139 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ C2×D139 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×D139 |
| commutator, cosocle, hypocenter | C5×C139 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C139 | C22 |
| LCS | G ▷ C5×C139 | |
| UCS | C1 ◁ C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1390 |
1420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13900, 21);