Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C271 ⋊ #556 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D271 |
| commutator, socle, cosocle | C22×C271 | C24 |
| Fitting | #124×C271 | C2 |
| prime radical | C2×D4×C271 | C22 |
| hypercenter | #124 | D271 |
| hypocenter | C271 | #556 |
| LCS | G ▷ C22×C271 ▷ C271 | |
| UCS | C1 ◁ C22 ◁ #124 | |
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8672 |
Polycyclic presentation:
2^6,271|b^2=ef,c^2=e,d^2=e,b^a=be,c^a=cf,d^b=de,g^c=g^270,g^d=g^2701915 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46849008, #46849010, #46849044, … |
| maximal normal subgroup of | #46849008, #46849010, #46849044, … |
| maximal quotient of | #46839254, #46839312, #46839316, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 1268);