Finite Group DatabasebetaFinite Group Databasebeta| order | 18676 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×AGL(1,𝔽29) |
| unambiguous semidirect product | #1181⋊(C7×C23) |
| unambiguous semidirect product | (C23×#1181)⋊C7 |
| Fitting, socle, Hall | C23×C29 ⋊ C4×C7 |
| derived, Sylow | C29 ⋊ C4×C7×C23 |
| Hall | C23×C29⋊C7 ⋊ C4 |
| Hall | C23×#1181 ⋊ C7 |
| Hall | C29⋊C7 ⋊ C4×C23 |
| Hall | #1181 ⋊ C7×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | AGL(1,𝔽29) |
| commutator, hypocenter | C29 | C4×C7×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C29 | C4×C7 |
| prime radical | C23×D29⋊C7 | C2 |
| cosocle | D29 | C2×C7×C23 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 667 |
667 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18676, 14);