Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | #2276 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C22×C42⋊C3 |
| commutator, hypocenter | #95 | C22×C9 |
| Frattini, socle, prime radical | C23×C3 | C22×A4 |
| Fitting | C3×#2276 | C3 |
| cosocle | C3×#95 | C22×C3 |
| hypercenter | C3×Q8 | C42⋊C3 |
| LCS | G ▷ #95 | |
| UCS | C1 ◁ C2×C3 ◁ C3×Q8 | |
249 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^2,3^2,2^5|a^2=g,b^2=g,c^3=d,e^2=h,f^2=ghi,b^a=bg,c^a=cgh,c^b=cgi,e^c=fgh,f^c=efg,h^c=ghi,i^c=h,f^e=fg108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153414);