Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C271 ⋊ #383 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D271 |
| commutator | C22×C271 | C22×C4 |
| Fitting | #95×C271 | C2 |
| socle, prime radical, cosocle | C23×C271 | C23 |
| hypercenter | #95 | D271 |
| hypocenter | C271 | #383 |
| LCS | G ▷ C22×C271 ▷ C271 | |
| UCS | C1 ◁ C23 ◁ #95 | |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17344 |
Polycyclic presentation:
2^6,271|a^2=f,b^2=de,c^2=d,b^a=bd,c^a=ce,g^c=g^2702728 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46834909, #46834913, #46834938, … |
| maximal normal subgroup of | #46834909, #46834913, #46834938, … |
| maximal quotient of | #46834588, #46834589, #46834590, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 416);