Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #1843 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#157 |
| commutator, socle, prime radical | C23×C32 | C22×C4 |
| Fitting | C32×#95 | C4 |
| cosocle | C22×C3⋊Dic3 | C23 |
| hypercenter | #95 | #157 |
| hypocenter | C32 | #1843 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #95 | |
434 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 102 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=f,b^2=d,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=hi,i^a=hi^2,c^b=cg,h^f=h^2,i^f=i^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 20205);