Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C191 ⋊ C2 |
| Sylow | C191 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D191 |
| commutator, socle | C2×C191 | C22×C8 |
| Fitting | M32×C191 | C2 |
| prime radical | #15690287 | C4 |
| cosocle | C8×C191 | C23 |
| hypercenter | M32 | D191 |
| hypocenter | C191 | #504 |
| LCS | G ▷ C2×C191 ▷ C191 | |
| UCS | C1 ◁ C8 ◁ M32 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=d,d^2=e,e^2=f,g^a=g^190,c^b=cf,g^c=g^1901940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37574354, #37574356, #37574359, … |
| maximal normal subgroup of | #37574354, #37574356, #37574359, … |
| maximal quotient of | #37574118, #37574119, #37574132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 967);