Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
| direct product | C16×#11764047 |
| derived, Sylow | C137 ⋊ C8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #10587739 |
| commutator, hypocenter | C137 | C8×C16 |
| Frattini | C2×C8 | C2×#10587739 |
| Fitting | C2×C16×C137 | C4 |
| socle, prime radical | C22×C137 | C4×C8 |
| cosocle | C8×Dic137 | C22 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C2×C16 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17536 |
1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 19419);