Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C9×H(5,𝔽2) ⋊ C2 |
| Sylow | C9 ⋊ #3484 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D9 |
| commutator, cosocle | C22×C9 | C25 |
| Frattini, socle | C22×C3 | C24×D3 |
| Fitting | C2×C9×H(5,𝔽2) | C2 |
| hypercenter | C2×H(5,𝔽2) | D9 |
| hypocenter | C9 | #3484 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
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,d^b=df,h^c=h^2i^2,i^c=i^2180 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#3484, #72268842, #72268904 |
| maximal normal subgroup of | D9×#3484, #72268842, #72268904 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 138287);