Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C9×#568 ⋊ C2 |
| Sylow | C9 ⋊ #3585 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×D36 |
| commutator, cosocle | C4×C9 | C25 |
| Frattini | C3×C4 | C24×D3 |
| Fitting | C9×#568 | C2 |
| socle | C2×C3 | C23×D12 |
| hypercenter | #568 | D9 |
| hypocenter | C9 | #3585 |
| LCS | G ▷ C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #568 | |
2196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|f^2=g,h^3=i,b^a=bf,e^a=eg,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=dg177 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#3585, #72268966, #72268983 |
| maximal normal subgroup of | D9×#3585, #72268966, #72268983 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153046);