Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #3107 |
390 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^66,f^c=fg1358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30750548, #30750550, #30750555, … |
| maximal normal subgroup of | #30750548, #30750550, #30750555, … |
| maximal quotient of | #30855868, #30858770, #30858792, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14581);