Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C22⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1788 |
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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=f,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^82,d^b=dg,h^b=h^821678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296590, #35296595, #35296604, … |
| maximal normal subgroup of | #35296590, #35296595, #35296604, … |
| maximal quotient of | #35295781, #35295794, #35295855, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4451);