Finite Group DatabasebetaFinite Group Databasebeta| order | 37636 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C97 · Schur multiplier (H2) = C1 |
| direct product | C97×#87604 |
| Fitting, socle, Sylow | C972 ⋊ C4 |
| derived | C97 ⋊ C4×C97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C97 | #87604 |
| commutator, hypocenter | C97 | C4×C97 |
| Frattini | C1 | G |
| Fitting, socle | C972 | C4 |
| prime radical | C97×D97 | C2 |
| cosocle | D97 | C2×C97 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C97 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 388 |
2716 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37636, 10);