Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #2108 |
184 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 141 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,d^2=f,f^2=g,h^a=h^82,c^b=cg1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35316060, #35316064, #35319237, … |
| maximal normal subgroup of | #35316060, #35316064, #35319237, … |
| maximal quotient of | #35313386, #35313393, M16×C83⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6107);