Finite Group DatabasebetaFinite Group Databasebeta| order | 26818 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | D53×C23⋊C11 |
| unambiguous semidirect product | C53⋊(C2×C23⋊C11) |
| unambiguous semidirect product | (C23×D53)⋊C11 |
| Fitting, socle, derived, Hall | C23×C53 ⋊ C2×C11 |
| Hall | C53×C23⋊C11 ⋊ C2 |
| Hall | C23×D53 ⋊ C11 |
| Sylow | C53 ⋊ C2×C23⋊C11 |
| 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 |
364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26818, 10);