Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C9 ⋊ #3458 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D9 |
| commutator, cosocle | C22×C9 | C25 |
| Frattini, socle | C22×C3 | C24×D3 |
| Fitting | C9×#543 | C2 |
| prime radical | C24×C3 | C22×D3 |
| hypercenter | #543 | D9 |
| hypocenter | C9 | #3458 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ #543 | |
1494 conjugacy classes of subgroups; only the 590 normal subgroups are shown.
This group has 1494 conjugacy classes of subgroups — too many to draw. Only its 590 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=g,c^2=g,e^2=f,h^3=i,b^a=bf,c^a=cg,d^a=df,c^b=cf,h^e=h^2i^2,i^e=i^2132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 135941);