Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C283 · Schur multiplier (H2) = C23×C4 |
| direct product | #390×C283 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C283 | C23 |
| commutator | C22 | C22×C4×C283 |
| Frattini, cosocle | C23 | C23×C283 |
| prime radical | C22×D4×C283 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C283 ◁ G | |
258 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9056 |
7924 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 71);