Finite Group DatabasebetaFinite Group Databasebeta| order | 36944 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×#22604437 |
| Fitting | C4×C2309 ⋊ C4 |
| derived, Sylow | C2309 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #22604437 |
| commutator, hypocenter | C2309 | C42 |
| Frattini | C2 | C2×#22604437 |
| Fitting | C4×C2309 | C4 |
| socle | C2×C2309 | C2×C4 |
| prime radical, cosocle | C2×D2309 | C22 |
| LCS | G ▷ C2309 | |
| UCS | C1 ◁ C4 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9236 |
2324 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36944, 44);