Finite Group DatabasebetaFinite Group Databasebeta| order | 26818 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C53⋊AGL(1,𝔽23) |
| unambiguous semidirect product | (C23⋊C11)⋊D53 |
| unambiguous semidirect product | D1219⋊C11 |
| Fitting, socle, derived, Hall | C23×C53 ⋊ C2×C11 |
| Hall | C53×C23⋊C11 ⋊ C2 |
| Hall | D1219 ⋊ C11 |
| Hall | C23⋊C11 ⋊ D53 |
| Sylow | C53 ⋊ AGL(1,𝔽23) |
| Sylow | C23 ⋊ C11×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C53 | C2×C11 |
| LCS | G ▷ C23×C53 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1219 |
Polycyclic presentation:
2,11,23,53|c^a=c^22,d^a=d^52,c^b=c^2361 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26818, 12);