Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C191 ⋊ #488 |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^b=g^190,g^c=g^1901352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570694, #37570696, #488×D191, … |
| maximal normal subgroup of | #37570694, #37570696, #488×D191, … |
| maximal quotient of | #37572650, #37573199, #37573206, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 903);