Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×#22582785 |
| derived, Sylow | C281 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | D281 |
| commutator, hypocenter | C281 | C2×C32 |
| Frattini | C16 | C2×D281 |
| Fitting | C2×C16×C281 | C2 |
| socle, prime radical | C22×C281 | C16 |
| cosocle | C16×C281 | C22 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C2×C16 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17984 |
4544 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×Dic281, C4×#22582785, #49093436, … |
| maximal normal subgroup of | C32×Dic281, C4×#22582785, #49093436, … |
| maximal quotient of | C4×#22582785, #49093441, #49093499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 381);