Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C3×C42 |
No aliases for this group.
| Sylow | C32 ⋊ #1726 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#157 |
| commutator | C2×C32 | C43 |
| Fitting | C32×#95 | C4 |
| socle, prime radical | C23×C32 | C22×C4 |
| cosocle | C22×C3⋊Dic3 | C23 |
| hypercenter | #95 | #157 |
| hypocenter | C32 | #1726 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #95 | |
506 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^7,3^2|a^2=d,b^2=e,c^2=f,d^2=g,h^a=hi,i^a=hi^2,c^b=cg,h^d=h^2,i^d=i^2120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17056);