Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C23×D4×C9 ⋊ C2 |
| Sylow | C9 ⋊ #3484 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D9 |
| commutator, cosocle | C22×C9 | C25 |
| Frattini, socle | C22×C3 | C24×D3 |
| Fitting | C23×D4×C9 | C2 |
| hypercenter | C23×D4 | D9 |
| hypocenter | C9 | #3484 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ C23×D4 | |
2850 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|h^3=i,b^a=bf,c^a=cg,e^a=ef,h^a=h^2i^2,i^a=i^2,d^b=df204 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#3484, #72268793, #72268878, … |
| maximal normal subgroup of | D9×#3484, #72268793, #72268878, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 138299);