Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C33 ⋊ C4⋊C8 |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^5,3^3|a^2=c,b^2=cd,c^2=e,d^2=e,b^a=bcd,f^a=g,g^a=f^2,h^a=h^2,f^b=fg^2,g^b=f^2g^2,f^c=f^2,g^c=g^248 conjugacy classes — view the full character table.
| maximal subgroup of | GO+(4,𝔽2)⋊(C3⋊C8), #13165090, #13165091, … |
| maximal normal subgroup of | GO+(4,𝔽2)⋊(C3⋊C8), #13165090, #13165091, … |
| maximal quotient of | #13155144, #13155146, #13155157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2771);