Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C191 ⋊ #489 |
100 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,c^b=cf,g^c=g^1901346 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #489×D191, C2×#27133021, #37582863, … |
| maximal normal subgroup of | #489×D191, C2×#27133021, #37582863, … |
| maximal quotient of | #37572652, #37573208, #37573211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 907);