Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #1740 |
420 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=e,b^2=f,c^2=g,b^a=bd,d^a=dg,e^b=eg,h^b=h^661364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30761043, #30761044, #30761292, … |
| maximal normal subgroup of | #30761043, #30761044, #30761292, … |
| maximal quotient of | #30745421, #30745427, #30745433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4242);