Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | H(3,ℤ/4)×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2098 |
210 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=d,b^2=de,d^2=g,f^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^b=dg,e^b=eg,f^b=fg,h^b=h^82,f^c=fg,h^c=h^82928 conjugacy classes — view the full character table.
| maximal subgroup of | #35317747, #35317752, #35317758, … |
| maximal normal subgroup of | #35317747, #35317752, #35317758, … |
| maximal quotient of | #35309374, #35309381, #35309386, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6064);