Finite Group DatabasebetaFinite Group Databasebeta| order | 29756 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C43 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C173 ⋊ C2×C43 |
| derived, Sylow | C173 ⋊ C22×C43 |
| Hall | C173⋊C43 ⋊ C22 |
| Hall | C2×D173 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D173⋊C43 |
| commutator, cosocle, hypocenter | C173 | C22×C43 |
| Frattini | C1 | G |
| Fitting, socle | C2×C173 | C2×C43 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29756, 9);