Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#585 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D3×A4 |
| commutator, cosocle, hypocenter | C3×Q8 | C24×C3 |
| Fitting | C3×#585 | C2×C3 |
| socle | C2×C3 | C24×A4 |
| hypercenter | #41 | D3×A4 |
| LCS | G ▷ C3×Q8 | |
| UCS | C1 ◁ C2 ◁ #41 | |
2500 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 2500 conjugacy classes of subgroups — too many to draw. Only its 251 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:
2^4,3,2^2,3,2|b^2=i,c^2=i,d^2=i,f^2=i,g^2=i,d^a=di,h^a=h^2,c^b=ci,f^e=fg,g^e=f,g^f=gi105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157829);