Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C191 ⋊ #365 |
42 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=d,b^2=c,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^190,d^b=df,g^b=g^1901346 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #365×D191, C2×#27132487, #37574291, … |
| maximal normal subgroup of | #365×D191, C2×#27132487, #37574291, … |
| maximal quotient of | #37570585, #37570620, C2×#27132487 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 373);