Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #11921467 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | H(3,𝔽4) ⋊ C3⋊D3 |
| derived | #5450⋊C3 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #5450⋊C3 | C2 |
| Frattini, socle | C22 | A4⋊S4 |
| Fitting | H(3,𝔽4) | C3⋊D3 |
| LCS | G ▷ #5450⋊C3 | |
| UCS | C1 | |
193 conjugacy classes of subgroups; only the 13 normal subgroups are shown.
This group has 193 conjugacy classes of subgroups — too many to draw. Only its 13 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 16 |
Polycyclic presentation:
2,3^2,2^6|b^a=b^2,c^a=c^2,d^a=de,f^a=fg,h^a=hi,f^b=fg,g^b=f,h^b=i,i^b=hi,d^c=de,e^c=d,h^c=i,i^c=hi,f^d=fh,g^d=ghi,f^e=fhi,g^e=gi17 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155478);