Finite Group DatabasebetaFinite Group Databasebeta| order | 27010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×D185 |
| unambiguous semidirect product | C5⋊(C73×D37) |
| unambiguous semidirect product | C37⋊(D5×C73) |
| Fitting, socle, Hall | C5×C37×C73 ⋊ C2 |
| derived, Hall | C5×C37 ⋊ C2×C73 |
| Hall | C37×C73 ⋊ D5 |
| Hall | C5×C73 ⋊ D37 |
| Sylow | C37 ⋊ D5×C73 |
| Sylow | C5 ⋊ C73×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | D185 |
| commutator, cosocle, hypocenter | C5×C37 | C2×C73 |
| Frattini | C1 | G |
| Fitting, socle | C5×C37×C73 | C2 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C73 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13505 |
6862 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27010, 7);