Finite Group DatabasebetaFinite Group Databasebeta| order | 19088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#23750848 |
| derived, Sylow | C1193 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #18012025 |
| commutator, hypocenter | C1193 | C2×C8 |
| Frattini | C2 | C2×#18012025 |
| Fitting, socle, prime radical | C22×C1193 | C4 |
| cosocle | Dic1193 | C22 |
| LCS | G ▷ C1193 | |
| UCS | C1 ◁ C22 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19088 |
1208 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#23750848, #50303027, C22⋊#23750848, … |
| maximal normal subgroup of | C4×#23750848, #50303027, C22⋊#23750848, … |
| maximal quotient of | C4×#23750848, C22⋊#23750848, C4⋊#23750848, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19088, 47);