Finite Group DatabasebetaFinite Group Databasebeta| order | 26404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C41 · Schur multiplier (H2) = C2 |
| direct product | C2×C41×D161 |
| unambiguous semidirect product | (C2×C7)⋊(C41×D23) |
| unambiguous semidirect product | (C2×C23)⋊(D7×C41) |
| Fitting, socle | C2×C7×C23×C41 ⋊ C2 |
| derived, Hall | C7×C23 ⋊ C22×C41 |
| Hall | C7×C23×C41 ⋊ C22 |
| Hall | C23×C41 ⋊ C2×D7 |
| Hall | C7×C41 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D7×C41 |
| Sylow | C7 ⋊ C2×C41×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C41 | D161 |
| commutator, cosocle, hypocenter | C7×C23 | C22×C41 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C23×C41 | C2 |
| LCS | G ▷ C7×C23 | |
| UCS | C1 ◁ C2×C41 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13202 |
6724 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26404, 26);