Finite Group DatabasebetaFinite Group Databasebeta| order | 19088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#18012025 |
| unambiguous semidirect product | (C2×#18012025)⋊C2 |
| Fitting | C22×C1193 ⋊ C4 |
| Sylow | C1193 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4772 |
Polycyclic presentation:
2^4,1193|a^2=d,b^a=bc,e^a=e^186,e^d=e^11921202 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50303030, #50303031, C2×C22⋊#18012025, … |
| maximal normal subgroup of | #50303030, #50303031, C2×C22⋊#18012025, … |
| maximal quotient of | (C2×#18012025)⋊C4, C22⋊#23750848, #50303029, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19088, 45);