Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C9×#99 ⋊ C2 |
| Sylow | C9 ⋊ #2021 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #63444 |
| commutator, cosocle | C24×C9 | C23 |
| Frattini | C24×C3 | C22×D3 |
| Fitting | C2×C9×#99 | C2 |
| socle | C22×C3 | #882 |
| hypercenter | C2×#99 | D9 |
| hypocenter | C9 | #2021 |
| LCS | G ▷ C24×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C2×#99 | |
957 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 957 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|h^3=i,b^a=bd,c^a=ce,f^a=fg,c^b=cf,h^b=h^2i^2,i^b=i^2,d^c=dg,h^c=h^2i^2,i^c=i^2114 conjugacy classes — view the full character table.
| maximal subgroup of | #72268777, #72268793, #72268822, … |
| maximal normal subgroup of | #72268777, #72268793, #72268822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 26802);