Finite Group DatabasebetaFinite Group Databasebeta| order | 23544 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C27 · Schur multiplier (H2) = C2 |
| direct product | C2×AGL(1,𝔽109) |
| Fitting, socle | C2×C109 ⋊ C4×C27 |
| derived, Sylow | C109 ⋊ C2×C4×C27 |
| Hall | #15668887 ⋊ C2×C4 |
| Hall | C2×#89137 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽109) |
| commutator, hypocenter | C109 | C2×C4×C27 |
| Frattini | C1 | G |
| Fitting, socle | C2×C109 | C4×C27 |
| prime radical | C2×D109⋊C3 | C2×C9 |
| cosocle | #11758281⋊C2 | C22×C3 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 218 |
218 conjugacy classes — view the full character table.
| holomorph of | C2×C109 |
Past the SmallGroups library coverage — no SmallGroups id.