Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2 |
| direct product | C2×C17×#11759818 |
| Fitting, socle | C2×C132×C17 ⋊ C2×C3 |
| derived, Sylow | C132 ⋊ C22×C3×C17 |
| Hall | C2×C13×C17×D13 ⋊ C3 |
| Hall | C17×#92789 ⋊ C22 |
| Hall | C132×C17 ⋊ C22×C3 |
| Hall | C2×C13×D13 ⋊ C3×C17 |
| Hall | #92789 ⋊ C22×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | #11759818 |
| commutator, cosocle, hypocenter | C132 | C22×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C2×C132×C17 | C2×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C2×C17 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2652 |
1360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 191);