Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #447×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3282 |
504 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^66,d^b=de,e^b=eg,h^b=h^66,e^d=eg662 conjugacy classes — view the full character table.
| maximal subgroup of | #3282×D67, C2×#22571920, D4×#14524062, … |
| maximal normal subgroup of | #3282×D67, C2×#22571920, D4×#14524062, … |
| maximal quotient of | #30845662, #30845677, #30845692, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 16221);