Finite Group DatabasebetaFinite Group Databasebeta| order | 36752 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×#22604030 |
| Fitting | C4×C2297 ⋊ C4 |
| derived, Sylow | C2297 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #22604030 |
| commutator, hypocenter | C2297 | C42 |
| Frattini | C2 | C2×#22604030 |
| Fitting | C4×C2297 | C4 |
| socle | C2×C2297 | C2×C4 |
| prime radical, cosocle | C2×D2297 | C22 |
| LCS | G ▷ C2297 | |
| UCS | C1 ◁ C4 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9188 |
2312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36752, 44);