Finite Group DatabasebetaFinite Group Databasebeta| order | 26452 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#13095555 |
| Fitting, socle, Hall | C17×C389 ⋊ C4 |
| derived, Sylow | C389 ⋊ C4×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #13095555 |
| commutator, hypocenter | C389 | C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C389 | C4 |
| prime radical | C17×D389 | C2 |
| cosocle | D389 | C2×C17 |
| LCS | G ▷ C389 | |
| UCS | C1 ◁ C17 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6613 |
1717 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26452, 6);