Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #11720758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting, derived | C32×C42 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C42 | C2×C3 |
| Frattini, socle | C22×C3 | D3×A4 |
| LCS | G ▷ C32×C42 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2,3,2^2,3^2,2^2|c^2=g,d^2=gh,c^a=cgh,d^a=dh,e^a=e^2,f^a=f^2,c^b=dg,d^b=cd,e^b=ef,g^b=gh,h^b=g34 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11720758, #13147226, #13147227, … |
| maximal normal subgroup of | C2×#11720758, #13147226, #13147227, … |
| maximal quotient of | #13136830, #13136833, #13136847, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 725);