Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C32×#123 ⋊ C22 |
| Sylow | C32 ⋊ #3484 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×#123 | C22 |
| hypercenter | #123 | D32 |
| hypocenter | C32 | #3484 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ #123 | |
3973 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
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^b=h^2,i^b=i^2,i^c=hi^2,i^d=hi^2,h^e=h^2,i^e=i^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 138372);