Finite Group DatabasebetaFinite Group Databasebeta| order | 27105 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#19129429 |
| Fitting, socle, Hall | C5×C13×C139 ⋊ C3 |
| derived, Hall | C13×C139 ⋊ C3×C5 |
| Hall | C5×C139 ⋊ C13⋊C3 |
| Sylow | C139 ⋊ C5×C13⋊C3 |
| Hall | C5×C13 ⋊ C139⋊C3 |
| Sylow | C13 ⋊ C5×C139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #19129429 |
| commutator, cosocle, hypocenter | C13×C139 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C139 | C3 |
| LCS | G ▷ C13×C139 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9035 |
3025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27105, 4);