Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #2378 |
464 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 213 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,b^2=e,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^82,c^b=cef,d^b=de1186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35301430, #35301434, #35301444, … |
| maximal normal subgroup of | #35301430, #35301434, #35301444, … |
| maximal quotient of | #35326025, #35326035, #35326049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7676);