Finite Group DatabasebetaFinite Group Databasebeta| order | 26934 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C67 |
| unambiguous semidirect product | C3⋊(C67⋊D67) |
| unambiguous semidirect product | C67⋊D201 |
| Fitting, socle, derived, Hall | C3×C672 ⋊ C2 |
| Sylow | C672 ⋊ D3 |
| Sylow | C3 ⋊ C67⋊D67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C672 | C2 |
| LCS | G ▷ C3×C672 | |
| UCS | C1 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13467 |
Polycyclic presentation:
2,3,67^2|b^a=b^2,c^a=c^66,d^a=d^666735 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26934, 23);