Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C4×C8×#3866 |
| Fitting | C4×C8×C37 ⋊ C4 |
| derived, Sylow | C37 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | #3866 |
| commutator, hypocenter | C37 | C42×C8 |
| Frattini | C2×C4 | C22×#3866 |
| Fitting | C4×C8×C37 | C4 |
| socle | C22×C37 | C2×C42 |
| prime radical | C22×D37 | C22×C4 |
| cosocle | C2×C4×D37 | C23 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C4×C8 | |
408 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 226 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1184 |
416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 20161);