Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #381×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2377 |
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 173 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=def,h^a=h^82,c^b=cef,d^b=de,h^b=h^821186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35301422, #35301426, #35301436, … |
| maximal normal subgroup of | #35301422, #35301426, #35301436, … |
| maximal quotient of | #35326026, #35326040, #35326041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7669);