Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #525×C131 ⋊ C2 |
| Sylow | C131 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D131 |
| commutator, socle, cosocle | C22×C131 | C25 |
| Frattini | C22 | C24×D131 |
| Fitting | #525×C131 | C2 |
| hypercenter | #525 | D131 |
| hypocenter | C131 | D4×#41 |
| LCS | G ▷ C22×C131 ▷ C131 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
1648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4192 |
Polycyclic presentation:
2^7,131|e^2=f,b^a=bf,c^a=cg,d^b=df,h^d=h^1301870 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 17993);