Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #322×C83 ⋊ C2 |
| Sylow | C83 ⋊ C8×M16 |
224 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 121 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,e^2=g,c^a=cf,h^b=h^82,h^c=h^821720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×M16×D83, C2×#24905742, #35369985, … |
| maximal normal subgroup of | C8×M16×D83, C2×#24905742, #35369985, … |
| maximal quotient of | #35293756, #35293784, #35294828, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2789);