Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #3407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×#157 |
| commutator, socle | C2×C32 | C23×C8 |
| Fitting, prime radical | C2×C32×#41 | C4 |
| cosocle | C3⋊(C3⋊C8) | C24 |
| hypercenter | C2×#41 | #157 |
| hypocenter | C32 | #3407 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C4 ◁ C2×#41 | |
626 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 238 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=e,e^2=f,f^2=g,d^a=dg,h^a=hi,i^a=hi^2,c^b=cg,h^e=h^2,i^e=i^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133424);