Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C83 ⋊ #2327 |
516 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 237 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=g,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^82,c^b=ce,h^b=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35301108, #35301112, #35301136, … |
| maximal normal subgroup of | #35301108, #35301112, #35301136, … |
| maximal quotient of | #35325664, #35325716, #35325764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7230);