Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C32×#135 ⋊ C22 |
| Sylow | C32 ⋊ #3584 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D32×D4 |
| commutator, cosocle | C32×C4 | C25 |
| Frattini | C4 | C23×D32 |
| Fitting | C32×#135 | C22 |
| socle | C2×C32 | C23×D4 |
| hypercenter | #135 | D32 |
| hypocenter | C32 | #3584 |
| LCS | G ▷ C32×C4 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #135 | |
2981 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|e^2=g,f^2=g,b^a=bf,f^a=fg,f^b=fg,d^c=dg,h^c=h^2,i^c=i^2,i^d=hi^2114 conjugacy classes — view the full character table.
| maximal subgroup of | #72222759, #72222833, #72222873, … |
| maximal normal subgroup of | #72222759, #72222833, #72222873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153013);