Finite Group DatabasebetaFinite Group Databasebeta| order | 19088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C1193 ⋊ M16 |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9544 |
Polycyclic presentation:
2^4,1193|a^2=c,c^2=d,b^a=bd,e^a=e^186,e^c=e^11921202 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50303032, #50303033, C2×#34061814, … |
| maximal normal subgroup of | #50303032, #50303033, C2×#34061814, … |
| maximal quotient of | #50303027, C22⋊#23750848, #50303039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19088, 49);