Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C32 ⋊ C2×#504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D32 |
| commutator, socle | C2×C32 | C23×C8 |
| Fitting | C32×#131 | C22 |
| prime radical | #41×C3⋊D3 | C4 |
| cosocle | C32×C8 | C24 |
| hypercenter | #131 | D32 |
| hypocenter | C32 | C2×#504 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C8 ◁ #131 | |
869 conjugacy classes of subgroups; only the 278 normal subgroups are shown.
This group has 869 conjugacy classes of subgroups — too many to draw. Only its 278 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,i^a=hi^2,c^b=cg,h^d=h^2,i^d=i^2180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133405);