Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #1434 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C2×D32 |
| commutator | C22×C32 | C2×C42 |
| Fitting | C23×C32×C4 | C22 |
| socle, prime radical, cosocle | C24×C32 | C23 |
| hypercenter | C23×C4 | D32 |
| hypocenter | C32 | #1434 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
1301 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=g,c^2=d,b^a=bd,c^a=ce,h^a=h^2,i^a=i^2,i^b=hi^2,i^c=hi^2192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7203);