Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C2×C16×D281 |
| Fitting | C2×C16×C281 ⋊ C2 |
| derived, Sylow | C281 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | D281 |
| commutator, hypocenter | C281 | C22×C16 |
| Frattini | C8 | C22×D281 |
| Fitting | C2×C16×C281 | C2 |
| socle | C22×C281 | C2×C8 |
| prime radical | C22×D281 | C8 |
| cosocle | C8×C281 | C23 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C2×C16 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8992 |
4544 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49093440, C4×C16×D281, #346×D281, … |
| maximal normal subgroup of | #49093440, C4×C16×D281, #346×D281, … |
| maximal quotient of | C4×C16×D281, C2×C16×Dic281, C22⋊C16×D281, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 960);