Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | #391×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2311 |
880 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 229 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=g,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,h^b=h^82,h^c=h^82,h^d=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35313513, #35313791, #35319390, … |
| maximal normal subgroup of | #35313513, #35313791, #35319390, … |
| maximal quotient of | #35325653, #35325704, #35325711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7101);