Finite Group DatabasebetaFinite Group Databasebeta| order | 26818 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×AGL(1,𝔽23) |
| unambiguous semidirect product | D23⋊(C11×C53) |
| unambiguous semidirect product | (C23⋊C11)⋊(C2×C53) |
| unambiguous semidirect product | (D23×C53)⋊C11 |
| Fitting, socle, Hall | C23×C53 ⋊ C2×C11 |
| derived, Sylow | C23 ⋊ C2×C11×C53 |
| Hall | C53×C23⋊C11 ⋊ C2 |
| Hall | D23×C53 ⋊ C11 |
| Hall | C23⋊C11 ⋊ C2×C53 |
| Hall | D23 ⋊ C11×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | AGL(1,𝔽23) |
| commutator, cosocle, hypocenter | C23 | C2×C11×C53 |
| Frattini | C1 | G |
| Fitting, socle | C23×C53 | C2×C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C53 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1219 |
1219 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26818, 11);