Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | #127×D191 |
| Fitting | #127×C191 ⋊ C2 |
| Sylow | C191 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D191 |
| commutator, socle, cosocle | C22×C191 | C24 |
| Fitting | #127×C191 | C2 |
| hypercenter | #127 | D191 |
| hypocenter | C191 | C2×#127 |
| LCS | G ▷ C22×C191 ▷ C191 | |
| UCS | C1 ◁ C22 ◁ #127 | |
498 conjugacy classes of subgroups.
1358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #331×D191, #37571186, #37571232, … |
| maximal normal subgroup of | #331×D191, #37571186, #37571232, … |
| maximal quotient of | #384×D191, #390×D191, #37575082, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1087);