Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×D8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3264 |
568 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^82,d^b=de,e^b=eg,e^d=eg1177 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3264×D83, C2×#24918943, #36279473, … |
| maximal normal subgroup of | #3264×D83, C2×#24918943, #36279473, … |
| maximal quotient of | #35393751, #35393871, #35393991, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15990);