Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | D4⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1639 |
308 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 59 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=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^82,d^b=df,e^b=eg,h^b=h^82,d^c=dg,e^c=eg1174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1639×D83, C2×#24906644, #35380093, … |
| maximal normal subgroup of | #1639×D83, C2×#24906644, #35380093, … |
| maximal quotient of | #35293192, #35293203, #35293261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3691);