Finite Group DatabasebetaFinite Group Databasebeta| order | 26404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C7⋊#4223 |
| unambiguous semidirect product | C7⋊(C23×#4223) |
| Fitting, socle, Hall | C7×C23×C41 ⋊ C4 |
| derived, Hall | C7×C41 ⋊ C4×C23 |
| Hall | C23×C41 ⋊ Dic7 |
| Hall | C7×C23 ⋊ #4223 |
| Sylow | C41 ⋊ C23×Dic7 |
| Sylow | C7 ⋊ C23×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C7⋊#4223 |
| commutator, hypocenter | C7×C41 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C7×C23×C41 | C4 |
| prime radical | C7×C23×D41 | C2 |
| cosocle | C7×D41 | C2×C23 |
| LCS | G ▷ C7×C41 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6601 |
1840 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26404, 13);