Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C32×C32 ⋊ C22 |
| Sylow | C32 ⋊ C2×M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C2×D32 |
| commutator, socle | C2×C32 | C22×C16 |
| Fitting | C32×C32 | C22 |
| prime radical | C2×D32 | C16 |
| cosocle | C32×C16 | C23 |
| hypercenter | C32 | D32 |
| hypocenter | C32 | C2×M64 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C16 ◁ C32 | |
241 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 241 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,i^b=hi^2,h^c=h^2,i^c=i^2192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34477);