Finite Group DatabasebetaFinite Group Databasebeta| order | 19072 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×#41×C149 ⋊ C2 |
| Sylow | C149 ⋊ #3524 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D149 |
| commutator, socle, cosocle | C22×C149 | C25 |
| Fitting | C4×#41×C149 | C2 |
| hypercenter | C4×#41 | D149 |
| hypocenter | C149 | #3524 |
| LCS | G ▷ C22×C149 ▷ C149 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
1030 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9536 |
Polycyclic presentation:
2^7,149|b^2=f,c^2=f,d^2=f,e^2=fg,b^a=bf,c^a=cg,e^a=ef,h^a=h^148,d^b=df3004 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19072, 18619);