Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C32 ⋊ C42×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D32 |
| commutator | C2×C32 | C22×C42 |
| Fitting | C32×#95 | C22 |
| socle, cosocle | C23×C32 | C24 |
| prime radical | C22×#626 | C22 |
| hypercenter | #95 | D32 |
| hypocenter | C32 | C42×D4 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #95 | |
1977 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=g,c^2=g,d^2=f,b^a=be,h^c=h^2,i^c=i^2,i^d=hi^2180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34821);