Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #419×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×#137 |
484 conjugacy classes of subgroups.
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,e^b=eg,h^c=h^82946 conjugacy classes — view the full character table.
| maximal subgroup of | #35410292, #35410294, #35410314, … |
| maximal normal subgroup of | #35410292, #35410294, #35410314, … |
| maximal quotient of | #35373825, #35373994, #35374025, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13325);