Finite Group DatabasebetaFinite Group Databasebeta| order | 36928 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C4×#22604432 |
| Fitting | C4×C577 ⋊ C16 |
| derived, Sylow | C577 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #22604432 |
| commutator, hypocenter | C577 | C4×C16 |
| Frattini | C2 | C2×#22604432 |
| Fitting | C4×C577 | C16 |
| socle | C2×C577 | C2×C16 |
| prime radical | C2×D577 | C2×C8 |
| cosocle | C2×#17987239 | C22 |
| LCS | G ▷ C577 | |
| UCS | C1 ◁ C4 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2308 |
208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36928, 1674);