Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2275 |
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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=g,c^2=f,b^a=be,d^a=de,c^b=ce,h^c=h^82,h^d=h^821708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35301298, #35301302, #35301312, … |
| maximal normal subgroup of | #35301298, #35301302, #35301312, … |
| maximal quotient of | #35325485, #35325489, #35325682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6870);