Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×#41×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3111 |
392 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^66,d^c=dg,f^c=fg1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3111×D67, C2×#22570318, #31724047, … |
| maximal normal subgroup of | #3111×D67, C2×#22570318, #31724047, … |
| maximal quotient of | #30855905, #30858847, #30858862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14619);