Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #504×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2170 |
146 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 65 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,c^2=e,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,d^b=dg,h^b=h^821696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35324965, #35324966, #35324970, … |
| maximal normal subgroup of | #35324965, #35324966, #35324970, … |
| maximal quotient of | C16×#13050575, #35316119, C16×#13050578, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6345);