Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C79 · Schur multiplier (H2) = C211×C42 |
| direct product | C22×H(3,𝔽4)×C79 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C79 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C79 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C79 ◁ G | |
10246 conjugacy classes of subgroups; only the 5774 normal subgroups are shown.
This group has 10246 conjugacy classes of subgroups — too many to draw. Only its 5774 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5056 |
6004 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 55676);