Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | #125×#3866 |
| Fitting | #125×C37 ⋊ C4 |
| Sylow | C37 ⋊ C4×#125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#3866 |
| commutator, socle | C22×C37 | C23×C4 |
| Fitting | #125×C37 | C4 |
| prime radical, cosocle | C22×D37 | C24 |
| hypercenter | #125 | #3866 |
| hypocenter | C37 | C4×#125 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #125 | |
484 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1184 |
182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 20979);