Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4⋊C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3076 |
388 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=e,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^66,f^c=fg,h^c=h^661358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30750703, #30750705, #30750710, … |
| maximal normal subgroup of | #30750703, #30750705, #30750710, … |
| maximal quotient of | #30855306, #30856782, #30857995, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14300);