Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #1288 |
152 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 57 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=d,b^2=e,c^2=fg,e^2=g,b^a=bc,c^a=cf,e^a=efg,d^b=dg,h^b=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1288×D83, C2×#24905327, #35294246, … |
| maximal normal subgroup of | #1288×D83, C2×#24905327, #35294246, … |
| maximal quotient of | #35290939, #35290949, #35290954, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2374);