Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | 2−1+4×C271 ⋊ C2 |
| Sylow | C271 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D271 |
| commutator, socle, cosocle | C2×C271 | C25 |
| Fitting | 2−1+4×C271 | C2 |
| hypercenter | 2−1+4 | D271 |
| hypocenter | C271 | #585 |
| LCS | G ▷ C2×C271 ▷ C271 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
810 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4336 |
Polycyclic presentation:
2^6,271|e^2=f,b^a=bf,d^a=df,c^b=cf,g^c=g^270,g^d=g^270,g^e=g^2702329 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46845711, #46845716, #46845734, … |
| maximal normal subgroup of | #46845711, #46845716, #46845734, … |
| maximal quotient of | #46849564, #46849566, #46849570, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 1386);