Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #2587 |
428 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=efg,c^2=g,d^2=f,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^821678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2587×D83, C2×#24912878, #35574758, … |
| maximal normal subgroup of | #2587×D83, C2×#24912878, #35574758, … |
| maximal quotient of | #35326874, #35327027, #35328234, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 9925);