Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #3323 |
402 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=eg,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^82,c^b=cg,d^b=de,f^c=fg1054 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3323×D83, C2×#24919679, #36281353, … |
| maximal normal subgroup of | #3323×D83, C2×#24919679, #36281353, … |
| maximal quotient of | #35420004, #35420806, #35421689, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16726);