Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #1534 |
196 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,b^2=f,d^2=g,e^2=f,b^a=bd,c^a=cg,d^a=df,h^a=h^82,d^b=dg,e^b=efg1174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296934, #35296937, #35296939, … |
| maximal normal subgroup of | #35296934, #35296937, #35296939, … |
| maximal quotient of | #35292484, #35292522, #35292684, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3137);