Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C271 ⋊ #554 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D271 |
| commutator, socle, cosocle | C22×C271 | C24 |
| Fitting | C4×D4×C271 | C2 |
| prime radical | C2×D4×C271 | C22 |
| hypercenter | C4×D4 | D271 |
| hypocenter | C271 | #554 |
| LCS | G ▷ C22×C271 ▷ C271 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
228 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 115 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|a^2=e,b^2=ef,d^2=e,b^a=be,c^a=cf,d^b=de,g^b=g^2702725 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46835434, #46835438, #46835496, … |
| maximal normal subgroup of | #46835434, #46835438, #46835496, … |
| maximal quotient of | #46839239, D4×C4⋊Dic271, #46839269, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 1256);