Finite Group DatabasebetaFinite Group Databasebeta| order | 19088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#23750841 |
| derived, Sylow | C1193 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D1193 |
| commutator, hypocenter | C1193 | C2×C8 |
| Frattini | C4 | C2×D1193 |
| Fitting | C2×C4×C1193 | C2 |
| socle, prime radical | C22×C1193 | C4 |
| cosocle | C4×C1193 | C22 |
| LCS | G ▷ C1193 | |
| UCS | C1 ◁ C2×C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19088 |
4784 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic1193, C4×#23750841, #50302882, … |
| maximal normal subgroup of | C8×Dic1193, C4×#23750841, #50302882, … |
| maximal quotient of | C4×#23750841, C22⋊#23750841, C4⋊#23750841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19088, 22);