Finite Group DatabasebetaFinite Group Databasebeta| order | 26404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D161⋊D41 |
| unambiguous semidirect product | D287⋊D23 |
| unambiguous semidirect product | D943⋊D7 |
| Fitting, socle, derived, Hall | C7×C23×C41 ⋊ C22 |
| Hall | C23×C41 ⋊ C2×D7 |
| Hall | C7×C41 ⋊ C2×D23 |
| Hall | C7×C23 ⋊ C2×D41 |
| Sylow | C41 ⋊ D7×D23 |
| Sylow | C23 ⋊ D7×D41 |
| Sylow | C7 ⋊ D23×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C23×C41 | C22 |
| LCS | G ▷ C7×C23×C41 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6601 |
Polycyclic presentation:
2^2,7,23,41|d^a=d^22,e^a=e^40,c^b=c^6,d^b=d^221705 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26404, 20);