Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #339×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1733 |
404 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 137 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=e,b^2=f,d^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^c=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1733×D83, C2×#24907171, #35401793, … |
| maximal normal subgroup of | #1733×D83, C2×#24907171, #35401793, … |
| maximal quotient of | #35293841, #35293847, #35293850, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4218);