Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×C271⋊C32 |
| unambiguous semidirect product | (C2×C271)⋊C32 |
| derived, Sylow | C271 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | D271 |
| commutator, hypocenter | C271 | C2×C32 |
| Frattini | C16 | C2×D271 |
| Fitting | C2×C16×C271 | C2 |
| socle, prime radical | C22×C271 | C16 |
| cosocle | C16×C271 | C22 |
| LCS | G ▷ C271 | |
| UCS | C1 ◁ C2×C16 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17344 |
4384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×Dic271, C4×C271⋊C32, #46834497, … |
| maximal normal subgroup of | C32×Dic271, C4×C271⋊C32, #46834497, … |
| maximal quotient of | C4×C271⋊C32, C22⋊(C271⋊C32), C4⋊(C271⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 381);