Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | H(3,𝔽4)×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1655 |
262 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,h^a=h^82,d^b=df,e^b=eg,d^c=dg,e^c=efg799 conjugacy classes — view the full character table.
| maximal subgroup of | #35325133, #35325134, #1655×D83, … |
| maximal normal subgroup of | #35325133, #35325134, #1655×D83, … |
| maximal quotient of | #35293102, #35293149, #35293162, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3799);