Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Fitting | C9×#585 ⋊ C2 |
| Sylow | C9 ⋊ 2−1+6 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C25×D9 |
| commutator, cosocle | C2×C9 | C26 |
| Frattini, socle | C2×C3 | C25×D3 |
| Fitting | C9×#585 | C2 |
| hypercenter | #585 | D9 |
| hypocenter | C9 | 2−1+6 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2 ◁ #585 | |
8694 conjugacy classes of subgroups; only the 3576 normal subgroups are shown.
This group has 8694 conjugacy classes of subgroups — too many to draw. Only its 3576 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|c^2=g,d^2=g,h^3=i,b^a=bg,f^a=fg,e^b=eg,d^c=dg,h^e=h^2i^2,i^e=i^2,h^f=h^2i^2,i^f=i^2201 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153300);