Finite Group DatabasebetaFinite Group Databasebeta| order | 26166 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C89 · Schur multiplier (H2) = C7 |
| direct product | C2×C89×#3862 |
| Fitting, socle, Hall | C2×C72×C89 ⋊ C3 |
| derived, Sylow | C72 ⋊ C2×C3×C89 |
| Hall | C72×C89 ⋊ C2×C3 |
| Hall | C2×C72 ⋊ C3×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C89 | #3862 |
| commutator, cosocle, hypocenter | C72 | C2×C3×C89 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C89 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C89 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3738 |
3382 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26166, 35);