Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×C4×D271 |
| Fitting | C23×C4×C271 ⋊ C2 |
| derived, Sylow | C271 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D271 |
| commutator, hypocenter | C271 | C24×C4 |
| Frattini | C2 | C24×D271 |
| Fitting | C23×C4×C271 | C2 |
| socle | C24×C271 | C22 |
| prime radical | C24×D271 | C2 |
| cosocle | C2×C271 | C25 |
| LCS | G ▷ C271 | |
| UCS | C1 ◁ C23×C4 | |
1362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8672 |
4384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D271)⋊#95, #46836273, C2×#95×D271, … |
| maximal normal subgroup of | (C2×D271)⋊#95, #46836273, C2×#95×D271, … |
| maximal quotient of | C22×C42×D271, C23×C4×Dic271, C22×C22⋊C4×D271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 1367);