Finite Group DatabasebetaFinite Group Databasebeta| order | 7857 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | H(3,𝔽3)×C97 ⋊ C3 |
| Sylow | C97 ⋊ #732 |
32 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,97|b^3=d^2,b^a=bc,c^a=cd,e^b=e^35369 conjugacy classes — view the full character table.
| maximal subgroup of | #732×C97⋊C3, C3×#21463364, #37555950, … |
| maximal normal subgroup of | #732×C97⋊C3, C3×#21463364, #37555950, … |
| maximal quotient of | #37555763, #37555764, #37555772, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7857, 34);