Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C37 ⋊ #2995 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#3866 |
| commutator, socle | C22×C37 | C23×C4 |
| Fitting, prime radical | #121×C37 | C4 |
| cosocle | C2×Dic37 | C24 |
| hypercenter | #121 | #3866 |
| hypocenter | C37 | #2995 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #121 | |
346 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^7,37|a^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^31,c^b=ceg,d^b=dg,h^f=h^36164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 21463);