Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #63419⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #63419⋊C4 |
| derived | C42⋊C9 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #63419⋊C2 |
| commutator, hypocenter | C42⋊C9 | C2×C4 |
| Frattini, socle | C23×C3 | C2×S4 |
| Fitting | C3×#384 | D3 |
| prime radical | C2×#63419 | C2 |
| cosocle | C2×C42⋊C9 | C22 |
| LCS | G ▷ C42⋊C9 | |
| UCS | C1 ◁ C2 | |
270 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^3,3^2,2^4|b^2=c,d^3=e,f^2=h,g^2=i,d^a=d^2e^2,e^a=e^2,f^a=fgi,g^a=gi,h^a=hi,f^b=fh,g^b=gi,f^d=gh,g^d=fg,h^d=i,i^d=hi48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153959);