Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #2985 |
322 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 161 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,b^2=e,c^2=e,f^2=g,b^a=be,d^a=de,c^b=ce,d^b=dg,h^b=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35300997, #35301001, #35301011, … |
| maximal normal subgroup of | #35300997, #35301001, #35301011, … |
| maximal quotient of | #35403156, #35403176, #35403484, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13604);