Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C9×#131 ⋊ C2 |
| Sylow | C9 ⋊ #3584 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D36 |
| commutator, cosocle | C4×C9 | C25 |
| Frattini | C3×C4 | C24×D3 |
| Fitting | C2×C9×#131 | C2 |
| socle | C2×C3 | C23×D12 |
| hypercenter | C2×#131 | D9 |
| hypocenter | C9 | #3584 |
| LCS | G ▷ C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C4 ◁ C2×#41 ◁ C2×#131 | |
2136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|e^2=g,f^2=g,h^3=i,b^a=bf,f^a=fg,h^a=h^2i^2,i^a=i^2,f^b=fg,h^b=h^2i^2,i^b=i^2,d^c=dg204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152982);