Finite Group DatabasebetaFinite Group Databasebeta| order | 19088 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×#18012025 |
| Fitting | C4×C1193 ⋊ C4 |
| derived, Sylow | C1193 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #18012025 |
| commutator, hypocenter | C1193 | C42 |
| Frattini | C2 | C2×#18012025 |
| Fitting | C4×C1193 | C4 |
| socle | C2×C1193 | C2×C4 |
| prime radical, cosocle | C2×D1193 | C22 |
| LCS | G ▷ C1193 | |
| UCS | C1 ◁ C4 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4772 |
1208 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#18012025, #50303026, #50303036, … |
| maximal normal subgroup of | C8×#18012025, #50303026, #50303036, … |
| maximal quotient of | (C2×#18012025)⋊C4, C8×#18012025, C4×#23750848, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19088, 44);