Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C32×#131 ⋊ C22 |
| Sylow | C32 ⋊ #3584 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D3×D12 |
| commutator, cosocle | C32×C4 | C25 |
| Frattini | C4 | C23×D32 |
| Fitting | C32×#131 | C22 |
| socle | C2×C32 | C23×D4 |
| hypercenter | #131 | D32 |
| hypocenter | C32 | #3584 |
| LCS | G ▷ C32×C4 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #131 | |
2977 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|e^2=g,f^2=g,b^a=bf,f^a=fg,h^a=h^2,i^a=h^2i,f^b=fg,h^b=h^2,i^b=i^2,d^c=dg,i^e=hi^2126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153011);