Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #1390 |
234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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,b^a=bc,c^a=cf,f^a=fg,d^b=df,h^b=h^82,d^c=dg928 conjugacy classes — view the full character table.
| maximal subgroup of | #1390×D83, C2×#24905580, #35319345, … |
| maximal normal subgroup of | #1390×D83, C2×#24905580, #35319345, … |
| maximal quotient of | #35291362, #35291398, #35291403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2627);