Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C32 ⋊ #1438 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C2×D32 |
| commutator | C23×C32 | C22×C4 |
| Fitting | C25×C32 | C22 |
| socle, cosocle | C24×C32 | C23 |
| prime radical | C23×#638 | C2 |
| hypercenter | C25 | D32 |
| hypocenter | C32 | #1438 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C24 ◁ C25 | |
3017 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=g,b^a=bd,c^a=ce,i^a=hi^2,c^b=cf,h^c=h^2,i^c=i^2156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7295);