Finite Group DatabasebetaFinite Group Databasebeta| order | 19072 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C149 · Schur multiplier (H2) = C24×C4 |
| direct product | C4⋊#95×C149 |
| unambiguous semidirect product | C4⋊(#95×C149) |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C149 | C23 |
| commutator | C22 | C2×C42×C149 |
| Frattini, cosocle | C24 | C23×C149 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C149 ◁ G | |
656 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19072 |
8344 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C149×#7025, C149×#7039, C149×#7189, … |
| maximal normal subgroup of | C149×#7025, C149×#7039, C149×#7189, … |
| maximal quotient of | C149×#7554, C149×#7557, C149×#10832, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19072, 167);