Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C32×#367 ⋊ C2 |
| Sylow | C32 ⋊ #2177 |
516 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=e,c^2=eg,d^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,d^b=df,f^b=fg,h^b=h^2,i^b=i^2,h^c=h^2,i^c=i^2120 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#2177, #72222637, C2×#11797807, … |
| maximal normal subgroup of | C3⋊D3×#2177, #72222637, C2×#11797807, … |
| maximal quotient of | #72254915, C2×#11797807, #72255432 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 31818);