Finite Group DatabasebetaFinite Group Databasebeta| order | 6368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C199 ⋊ C2 |
| Sylow | C199 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,199|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^198,d^b=de1001 conjugacy classes — view the full character table.
| maximal subgroup of | #27164184, #27164185, #27164189, … |
| maximal normal subgroup of | #27164184, #27164185, #27164189, … |
| maximal quotient of | #27164017, #27164023, #27164058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6368, 172);