Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C191 ⋊ #393 |
202 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,191|a^2=d,b^2=d,b^a=bd,c^a=ce,c^b=cf,g^b=g^1901922 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570540, #37570542, #37571472, … |
| maximal normal subgroup of | #37570540, #37570542, #37571472, … |
| maximal quotient of | #37570763, #37570765, #37570776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 461);