Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #405×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2949 |
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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,b^2=g,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^82,e^b=eg,h^b=h^82,d^c=dg1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35418309, #35418311, #35420317, … |
| maximal normal subgroup of | #35418309, #35418311, #35420317, … |
| maximal quotient of | #35373871, #35374086, #35374095, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13371);