Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C191 ⋊ M64 |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^1903080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570655, #37570656, #37570659, … |
| maximal normal subgroup of | #37570655, #37570656, #37570659, … |
| maximal quotient of | #37570654, #37570658, #37570716, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 383);