Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C23 | D3×S4 |
| commutator | C2×C3×A4 | C42 |
| Fitting, socle | C25×C3 | C2×D3 |
| prime radical, cosocle | C23×C3×A4 | C22 |
| hypocenter | C3×A4 | #95 |
| LCS | G ▷ C2×C3×A4 ▷ C3×A4 | |
| UCS | C1 ◁ C23 | |
876 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^5,3^2,2^2|a^2=e,b^2=c,b^a=bd,g^a=g^2,f^b=f^2,h^b=hi,h^f=i,i^f=hi96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154755);