Finite Group DatabasebetaFinite Group Databasebeta| order | 27202 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C29 · Schur multiplier (H2) = C1 |
| direct product | C7×C29×D67 |
| unambiguous semidirect product | C67⋊(C2×C7×C29) |
| Fitting, socle, Hall | C7×C29×C67 ⋊ C2 |
| derived, Sylow | C67 ⋊ C2×C7×C29 |
| Hall | C29×C67 ⋊ C2×C7 |
| Hall | C7×C67 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C29 | D67 |
| commutator, cosocle, hypocenter | C67 | C2×C7×C29 |
| Frattini | C1 | G |
| Fitting, socle | C7×C29×C67 | C2 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C7×C29 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13601 |
7105 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27202, 3);