Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ #131 |
341 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|a^2=d,d^2=e,f^a=f^2,g^a=g^2,c^b=ce,g^f=gh100 conjugacy classes — view the full character table.
| maximal subgroup of | #13136955, #13141060, #13141061, … |
| maximal normal subgroup of | #13136955, #13141060, #13141061, … |
| maximal quotient of | #13144387, #13144390, #13144391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1836);