Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C32×#120 ⋊ C22 |
| Sylow | C32 ⋊ #3025 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D3×#937 |
| commutator, cosocle | C23×C32 | C24 |
| Frattini | C23 | C22×D32 |
| Fitting | C32×#120 | C22 |
| socle | C2×C32 | C2×#120 |
| hypercenter | #120 | D32 |
| hypocenter | C32 | #3025 |
| LCS | G ▷ C23×C32 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ #120 | |
1631 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|d^2=g,b^a=be,c^a=cf,f^b=fg,e^c=eg,h^c=h^2,i^c=i^2,i^d=hi^290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99321);