Finite Group DatabasebetaFinite Group Databasebeta| order | 19232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#23751259 |
| derived, Sylow | C601 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D601 |
| commutator, hypocenter | C601 | C2×C16 |
| Frattini | C8 | C2×D601 |
| Fitting | C2×C8×C601 | C2 |
| socle, prime radical | C22×C601 | C8 |
| cosocle | C8×C601 | C22 |
| LCS | G ▷ C601 | |
| UCS | C1 ◁ C2×C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19232 |
4832 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×Dic601, C4×#23751259, #50308451, … |
| maximal normal subgroup of | C16×Dic601, C4×#23751259, #50308451, … |
| maximal quotient of | C4×#23751259, C22⋊#23751259, C4⋊#23751259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19232, 84);