Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #2987 |
314 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 157 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=e,c^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,c^b=ceg,d^b=dg,h^b=h^821186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298810, #35298813, #35299355, … |
| maximal normal subgroup of | #35298810, #35298813, #35299355, … |
| maximal quotient of | #35403167, #35403185, #35403499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13615);