Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C32 ⋊ C4×#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C2×D32 |
| commutator | C2×C32 | C43 |
| Fitting | C23×C32×C4 | C22 |
| socle, prime radical, cosocle | C24×C32 | C23 |
| hypercenter | C23×C4 | D32 |
| hypocenter | C32 | C4×#95 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
1753 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^7,3^2|a^2=e,b^2=f,c^2=g,b^a=bd,i^b=hi^2,h^c=h^2,i^c=i^2192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7157);