Finite Group DatabasebetaFinite Group Databasebeta| order | 26828 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#13083443 |
| Fitting, socle, Hall | C19×C353 ⋊ C4 |
| derived, Sylow | C353 ⋊ C4×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #13083443 |
| commutator, hypocenter | C353 | C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C353 | C4 |
| prime radical | C19×D353 | C2 |
| cosocle | D353 | C2×C19 |
| LCS | G ▷ C353 | |
| UCS | C1 ◁ C19 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6707 |
1748 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26828, 6);