Finite Group DatabasebetaFinite Group Databasebeta| order | 19088 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1193 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #18012025 |
| commutator, hypocenter | C1193 | C16 |
| Fitting | C4×C1193 | C4 |
| socle, prime radical | C2×C1193 | C8 |
| cosocle | #23750841 | C2 |
| LCS | G ▷ C1193 | |
| UCS | C1 ◁ C4 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19088 |
Polycyclic presentation:
2^4,1193|a^2=b,b^2=c,c^2=d,e^a=e^186,e^b=e^11921208 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#34061808, #50303045, #50303046, … |
| maximal normal subgroup of | C2×#34061808, #50303045, #50303046, … |
| maximal quotient of | #50303022, C2×#34061808 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19088, 43);