Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×#41×C137 ⋊ C2 |
| Sylow | C137 ⋊ #3455 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D137 |
| commutator, socle, cosocle | C22×C137 | C25 |
| Frattini | C22 | C24×D137 |
| Fitting | C4×#41×C137 | C2 |
| hypercenter | C4×#41 | D137 |
| hypocenter | C137 | #3455 |
| LCS | G ▷ C22×C137 ▷ C137 | |
| UCS | C1 ◁ C2×C4 ◁ C4×#41 | |
1040 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4384 |
Polycyclic presentation:
2^7,137|b^2=g,e^2=f,b^a=bf,c^a=cg,d^a=df,c^b=cf,h^c=h^1362764 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 17895);