Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C271 ⋊ #557 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D271 |
| commutator, socle, prime radical, cosocle | C22×C271 | C24 |
| Fitting | C4×Q8×C271 | C2 |
| hypercenter | C4×Q8 | D271 |
| hypocenter | C271 | #557 |
| LCS | G ▷ C22×C271 ▷ C271 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17344 |
Polycyclic presentation:
2^6,271|a^2=f,b^2=e,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,g^c=g^2702725 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46849044, #46849050, #46849055, … |
| maximal normal subgroup of | #46849044, #46849050, #46849055, … |
| maximal quotient of | Q8×Dic271⋊C4, #46839282, #46839285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 1275);