Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #2849 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×C3⋊D3 |
| commutator, socle, cosocle | C23×C32 | C24 |
| Fitting, prime radical | C2×C32×#120 | C2 |
| hypercenter | C2×#120 | C3⋊D3 |
| hypocenter | C32 | #2849 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
3306 conjugacy classes of subgroups; only the 457 normal subgroups are shown.
This group has 3306 conjugacy classes of subgroups — too many to draw. Only its 457 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=e,b^a=be,c^a=cf,d^a=dg,h^c=h^2,i^c=i^2156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 90259);