Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#104×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3018 |
724 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^66,e^b=eg,f^b=fg,e^c=eg,h^c=h^66956 conjugacy classes — view the full character table.
| maximal subgroup of | #30861790, #30861795, #30861801, … |
| maximal normal subgroup of | #30861790, #30861795, #30861801, … |
| maximal quotient of | #30827939, #30827990, #30828041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13861);