Finite Group DatabasebetaFinite Group Databasebeta| order | 6112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C191 ⋊ C2 |
| Sylow | C191 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,191|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^190,d^b=de961 conjugacy classes — view the full character table.
| maximal subgroup of | #27132829, #27132830, #27132834, … |
| maximal normal subgroup of | #27132829, #27132830, #27132834, … |
| maximal quotient of | #27132662, #27132668, #27132703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6112, 172);