Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C3 |
No aliases for this group.
| Fitting | C2×C32×H(5,𝔽2) ⋊ C2 |
| Sylow | C32 ⋊ #3498 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×C3⋊D3 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C2×C32×H(5,𝔽2) | C2 |
| hypercenter | C2×H(5,𝔽2) | C3⋊D3 |
| hypocenter | C32 | #3498 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
5244 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|c^2=g,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^c=h^2,i^c=i^2180 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#3498, #72214562, #72214648 |
| maximal normal subgroup of | C3⋊D3×#3498, #72214562, #72214648 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 139949);