Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C8 |
| direct product | C2×C8×#11764047 |
| derived, Sylow | C137 ⋊ C2×C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | #10587739 |
| commutator, hypocenter | C137 | C2×C82 |
| Frattini | C2×C4 | C22×#10587739 |
| Fitting | C22×C8×C137 | C4 |
| socle, prime radical | C23×C137 | C42 |
| cosocle | C4×Dic137 | C23 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C22×C8 | |
280 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, 19701);