Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C9×#525 ⋊ C2 |
| Sylow | C9 ⋊ #3025 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #63499 |
| commutator, cosocle | C23×C9 | C24 |
| Frattini | C23×C3 | C23×D3 |
| Fitting | C9×#525 | C2 |
| socle | C2×C3 | C2×#937 |
| hypercenter | #525 | D9 |
| hypocenter | C9 | #3025 |
| LCS | G ▷ C23×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #525 | |
1149 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|d^2=g,h^3=i,b^a=be,c^a=cf,f^b=fg,e^c=eg,h^c=h^2i^2,i^c=i^2144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99309);