Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C8×C191 ⋊ C2 |
| Sylow | C191 ⋊ #432 |
110 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=e,c^2=d,e^2=f,b^a=bd,c^a=cf,g^b=g^190,g^c=g^1901928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570951, #37570953, #37570961, … |
| maximal normal subgroup of | #37570951, #37570953, #37570961, … |
| maximal quotient of | #37572267, #37572281, #37572375, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 605);