Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C131 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D131 |
| commutator, socle | C2×C131 | C24×C4 |
| Fitting, prime radical | #585×C131 | C2 |
| cosocle | C4×C131 | C25 |
| hypercenter | #585 | D131 |
| hypocenter | C131 | #3573 |
| LCS | G ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C4 ◁ #585 | |
1424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4192 |
Polycyclic presentation:
2^7,131|a^2=f,f^2=g,h^a=h^130,e^b=eg,d^c=dg2278 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 19222);