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 ⋊ #436 |
122 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,c^b=cf,g^b=g^190,g^c=g^1901928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37571346, #37571348, #37571360, … |
| maximal normal subgroup of | #37571346, #37571348, #37571360, … |
| maximal quotient of | #37571404, #37571409, #37571416, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 626);