Finite Group DatabasebetaFinite Group Databasebeta| order | 29844 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C4×#21418661 |
| Fitting, Hall | C4×C829 ⋊ C9 |
| derived, Sylow | C829 ⋊ C4×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #21418661 |
| commutator, hypocenter | C829 | C4×C9 |
| Frattini | C2 | C2×#21418661 |
| Fitting | C4×C829 | C9 |
| socle | C2×C829 | C2×C9 |
| prime radical, cosocle | C2×C829⋊C3 | C2×C3 |
| LCS | G ▷ C829 | |
| UCS | C1 ◁ C4 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3316 |
404 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29844, 21);