Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #11721950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C23 |
No aliases for this group.
| derived | C22⋊(C22⋊C27) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C22⋊(C22⋊C27) | C2 |
| Frattini | C9 | #1020 |
| Fitting | C24×C9 | D3 |
| socle | C24×C3 | D9 |
| LCS | G ▷ C22⋊(C22⋊C27) | |
| UCS | C1 | |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2,3^3,2^4|b^3=cd,c^3=d^2,b^a=b^2c^2,c^a=c^2d,d^a=d^2,e^a=f,f^a=e,g^a=h,h^a=g,e^b=f,f^b=ef,g^b=gh,h^b=g42 conjugacy classes — view the full character table.
| maximal subgroup of | #11721950⋊C2, C2×#11721950, #72229294, … |
| maximal normal subgroup of | #11721950⋊C2, C2×#11721950, #72229320 |
| maximal quotient of | #13145312, #13145313, #13145314, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1917);