Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #1839 |
240 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^822680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35290939, #35290940, #35290950, … |
| maximal normal subgroup of | #35290939, #35290940, #35290950, … |
| maximal quotient of | #35298124, #35298128, #35310009, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4653);