Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #3164 |
340 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=e,b^2=e,c^2=fg,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^c=h^66758 conjugacy classes — view the full character table.
| maximal subgroup of | #30914733, #30914737, #30914744, … |
| maximal normal subgroup of | #30914733, #30914737, #30914744, … |
| maximal quotient of | #30856279, #30859194, #30859208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15044);