Finite Group DatabasebetaFinite Group Databasebeta| order | 18676 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C23×C29 ⋊ C22×C7 |
| Hall | C23×C29⋊C7 ⋊ C22 |
| Hall | D23×D29 ⋊ C7 |
| Hall | C29⋊C7 ⋊ C2×D23 |
| Sylow | C29 ⋊ C2×C7×D23 |
| Sylow | C23 ⋊ C2×D29⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C29 | C22×C7 |
| LCS | G ▷ C23×C29 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 667 |
208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18676, 16);