Finite Group DatabasebetaFinite Group Databasebeta| order | 34688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C2×C32×D271 |
| Fitting | C2×C32×C271 ⋊ C2 |
| derived, Sylow | C271 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D271 |
| commutator, hypocenter | C271 | C22×C32 |
| Frattini | C16 | C22×D271 |
| Fitting | C2×C32×C271 | C2 |
| socle | C22×C271 | C2×C16 |
| prime radical | C22×D271 | C16 |
| cosocle | C16×C271 | C23 |
| LCS | G ▷ C271 | |
| UCS | C1 ◁ C2×C32 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17344 |
8768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34688, 6798);