Finite Group DatabasebetaFinite Group Databasebeta| order | 19072 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C149 · Schur multiplier (H2) = C24×C4 |
| direct product | #2352×C149 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C149 | C24 |
| commutator | C22 | C23×C4×C149 |
| Frattini, cosocle | C23 | C24×C149 |
| prime radical | C22×D4×C149 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C149 ◁ G | |
660 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9536 |
7450 conjugacy classes. The character table is too large to display.
| maximal quotient of | C22⋊C4×C4⋊C4×C149, C149×#13801, C149×#13804, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19072, 1084);