Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C3 |
No aliases for this group.
| Fitting | C32×#518 ⋊ C2 |
| Sylow | C32 ⋊ #3484 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×C3⋊D3 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×#518 | C2 |
| hypercenter | #518 | C3⋊D3 |
| hypocenter | C32 | #3484 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ #518 | |
5700 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|b^a=bf,c^a=cg,e^a=ef,h^a=h^2,i^a=i^2,d^b=df,h^c=h^2,i^c=i^2180 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#3484, #72214593, #72214828, … |
| maximal normal subgroup of | C3⋊D3×#3484, #72214593, #72214828, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 138303);