Finite Group DatabasebetaFinite Group Databasebeta| order | 34404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C47×C61 ⋊ C22×C3 |
| Hall | D47×D61 ⋊ C3 |
| Hall | C47×C61⋊C3 ⋊ C22 |
| Hall | C61⋊C3 ⋊ C2×D47 |
| Sylow | C61 ⋊ C2×C3×D47 |
| Sylow | C47 ⋊ C2×D61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C47×C61 | C22×C3 |
| LCS | G ▷ C47×C61 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2867 |
400 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34404, 16);