Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #2574 |
436 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=eg,b^2=eg,c^2=e,d^2=f,b^a=be,c^a=cf,d^a=de,h^a=h^82,c^b=cg1678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2574×D83, C2×#24912737, #35574758, … |
| maximal normal subgroup of | #2574×D83, C2×#24912737, #35574758, … |
| maximal quotient of | #35326730, #35326833, #35327382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 9784);