Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #125×C251 ⋊ C2 |
| Sylow | C251 ⋊ #552 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D251 |
| commutator, socle, cosocle | C22×C251 | C24 |
| Fitting | #125×C251 | C2 |
| prime radical | C2×D1004 | C22 |
| hypercenter | #125 | D251 |
| hypocenter | C251 | #552 |
| LCS | G ▷ C22×C251 ▷ C251 | |
| UCS | C1 ◁ C22 ◁ #125 | |
214 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8032 |
Polycyclic presentation:
2^6,251|a^2=e,b^2=f,c^2=e,b^a=be,c^a=cf,d^b=de,g^d=g^2501775 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #552×D251, C2×#30632369, #44563917, … |
| maximal normal subgroup of | #552×D251, C2×#30632369, #44563917, … |
| maximal quotient of | #44553218, #44553220, #44553231, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 1231);