Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | H(3,𝔽4)×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2199 |
270 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|b^a=bd,c^a=ce,f^a=fg,h^a=h^82,c^b=cg,e^b=efg,d^c=df,e^d=eg796 conjugacy classes — view the full character table.
| maximal subgroup of | #35325133, #35325135, #35325140, … |
| maximal normal subgroup of | #35325133, #35325135, #35325140, … |
| maximal quotient of | #35316451, #35316491, #35316620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6511);