Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C191 · Schur multiplier (H2) = C24 |
| direct product | #552×C191 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C191 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C191 |
| prime radical | C2×D4×C191 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C191 ◁ G | |
214 conjugacy classes of subgroups.
4775 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3296×C191, #3300×C191, #3310×C191, … |
| maximal normal subgroup of | #3296×C191, #3300×C191, #3310×C191, … |
| maximal quotient of | #2343×C191, #2344×C191, #2346×C191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 233);