Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1628 |
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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^2=g,c^2=fg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^82,d^b=df,e^b=eg,h^b=h^82,d^c=dg,e^c=eg,h^c=h^821174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1628×D83, C2×#24906576, #35380171, … |
| maximal normal subgroup of | #1628×D83, C2×#24906576, #35380171, … |
| maximal quotient of | #35293140, #35293159, #35293171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3623);