Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #11720744 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, derived | C42×C9 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C42×C9 | C2×C3 |
| Frattini, socle | C22×C3 | D3×A4 |
| LCS | G ▷ C42×C9 | |
| UCS | C1 | |
63 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2,3,2^2,3,2^2,3|c^2=g,d^2=f,e^3=h,c^a=cfg,d^a=dg,e^a=e^2h^2,h^a=h^2,c^b=cd,d^b=cf,e^b=eh^2,f^b=g,g^b=fg34 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11720744, #13147120, #13147121, … |
| maximal normal subgroup of | C2×#11720744, #13147120, #13147121, … |
| maximal quotient of | #13136800, #13136808, #13136815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 711);