Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C8×Dic281 |
| derived, Sylow | C281 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D281 |
| commutator, hypocenter | C281 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D281 |
| Fitting | C22×C8×C281 | C2 |
| socle, prime radical | C23×C281 | C2×C4 |
| cosocle | C2×C4×C281 | C23 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C22×C8 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17984 |
4544 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49093380, #49093384, C4×C8×Dic281, … |
| maximal normal subgroup of | #49093380, #49093384, C4×C8×Dic281, … |
| maximal quotient of | C2×C8×#14555886, C2×#31823185, C8×#17985122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 494);