Finite Group DatabasebetaFinite Group Databasebeta| order | 26660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C31×C43 ⋊ C22×C5 |
| Hall | C43×ΓL(1,𝔽32) ⋊ C22 |
| Hall | D31×D43 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C2×D43 |
| Sylow | C43 ⋊ C2×D31⋊C5 |
| Sylow | C31 ⋊ C2×C5×D43 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C43 | C22×C5 |
| LCS | G ▷ C31×C43 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1333 |
299 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26660, 14);