Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C191 · Schur multiplier (H2) = C25 |
| direct product | #578×C191 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C191 | C22×D4 |
| commutator, Frattini, cosocle | C4 | C24×C191 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C191 ◁ #41×C191 ◁ G | |
248 conjugacy classes of subgroups.
4202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 259);