Finite Group DatabasebetaFinite Group Databasebeta| order | 37377 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C4153⋊C3 |
| unambiguous semidirect product | C4153⋊C32 |
| unambiguous semidirect product | (C3×C4153)⋊C3 |
| Fitting, socle | C3×C4153 ⋊ C3 |
| derived, Sylow | C4153 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C4153⋊C3 |
| commutator, cosocle, hypocenter | C4153 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C4153 | C3 |
| LCS | G ▷ C4153 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12459 |
4161 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37377, 3);