Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #3152 |
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 157 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,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^82,d^b=dg,h^b=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35301919, #35301921, #35301960, … |
| maximal normal subgroup of | #35301919, #35301921, #35301960, … |
| maximal quotient of | #35392260, #35392304, #35392343, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14970);