Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C23×#14555513 |
| derived, Sylow | C137 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #10587739 |
| commutator, hypocenter | C137 | C23×C16 |
| Frattini | C4 | C23×#10587739 |
| Fitting | C23×C4×C137 | C4 |
| socle, prime radical | C24×C137 | C8 |
| cosocle | #11764040 | C24 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C23×C4 | |
440 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, 21469);