Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #349×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2115 |
220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 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=e,e^2=f,f^2=g,b^a=bd,d^a=dg,c^b=cg,e^b=eg,h^c=h^82946 conjugacy classes — view the full character table.
| maximal subgroup of | #35313703, #35313705, #35313707, … |
| maximal normal subgroup of | #35313703, #35313705, #35313707, … |
| maximal quotient of | #35313467, #35313539, #35313607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6129);