Finite Group DatabasebetaFinite Group Databasebeta| order | 37792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×#17990007 |
| unambiguous semidirect product | D1181⋊(C22×C4) |
| Fitting, socle | C23×C1181 ⋊ C4 |
| derived, Sylow | C1181 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #17990007 |
| commutator, hypocenter | C1181 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C1181 | C4 |
| prime radical | C23×D1181 | C2 |
| cosocle | D1181 | C24 |
| LCS | G ▷ C1181 | |
| UCS | C1 ◁ C23 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9448 |
2392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37792, 235);