Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C32×#137 ⋊ C22 |
| Sylow | C32 ⋊ C2×#578 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D32×D4 |
| commutator, cosocle | C32×C4 | C25 |
| Frattini | C4 | C23×D32 |
| Fitting | C32×#137 | C22 |
| socle | C2×C32 | C23×D4 |
| hypercenter | #137 | D32 |
| hypocenter | C32 | C2×#578 |
| LCS | G ▷ C32×C4 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #137 | |
2945 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=g,b^2=g,f^2=g,b^a=bf,f^a=fg,i^a=hi^2,f^b=fg,d^c=dg,i^d=hi^2,h^e=h^2,i^e=i^299 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152934);