Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×M16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2923 |
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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=f,c^2=e,f^2=g,b^a=be,c^a=cg,h^a=h^82,d^b=dg,h^b=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35301228, #35301232, #35301235, … |
| maximal normal subgroup of | #35301228, #35301232, #35301235, … |
| maximal quotient of | #35401896, #35401942, #35402302, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13162);