Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×C8×D271 |
| Fitting | C22×C8×C271 ⋊ C2 |
| derived, Sylow | C271 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D271 |
| commutator, hypocenter | C271 | C23×C8 |
| Frattini | C4 | C23×D271 |
| Fitting | C22×C8×C271 | C2 |
| socle | C23×C271 | C2×C4 |
| prime radical | C23×D271 | C4 |
| cosocle | C4×C271 | C24 |
| LCS | G ▷ C271 | |
| UCS | C1 ◁ C22×C8 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8672 |
4384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #336×D271, #46836059, #340×D271, … |
| maximal normal subgroup of | #336×D271, #46836059, #340×D271, … |
| maximal quotient of | C2×C4×C8×D271, C22×C8×Dic271, C2×C22⋊C8×D271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 1305);