Finite Group DatabasebetaFinite Group Databasebeta| order | 26404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D23×D41 |
| unambiguous semidirect product | (C41×D23)⋊(C2×C7) |
| unambiguous semidirect product | (C23×D41)⋊(C2×C7) |
| unambiguous semidirect product | D943⋊(C2×C7) |
| Fitting, socle, Hall | C7×C23×C41 ⋊ C22 |
| derived, Hall | C23×C41 ⋊ C22×C7 |
| Hall | C7×C41 ⋊ C2×D23 |
| Hall | C7×C23 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×C7×D23 |
| Sylow | C23 ⋊ C2×C7×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D23×D41 |
| commutator, cosocle, hypocenter | C23×C41 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C23×C41 | C22 |
| LCS | G ▷ C23×C41 | |
| UCS | C1 ◁ C7 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6601 |
2002 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26404, 12);