Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C137 ⋊ #2369 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D137 |
| commutator | C22×C137 | C23×C4 |
| Fitting | #389×C137 | C2 |
| socle, prime radical, cosocle | C23×C137 | C24 |
| hypercenter | #389 | D137 |
| hypocenter | C137 | #2369 |
| LCS | G ▷ C22×C137 ▷ C137 | |
| UCS | C1 ◁ C23 ◁ #389 | |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17536 |
Polycyclic presentation:
2^7,137|a^2=g,b^2=fg,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,h^d=h^1361954 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 7596);