Finite Group DatabasebetaFinite Group Databasebeta| order | 36100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C361 · Schur multiplier (H2) = C5 |
| direct product | #1044×C361 |
| Fitting, Hall | C52×C361 ⋊ C4 |
| derived, Sylow | C52 ⋊ C4×C361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C361 | #1044 |
| commutator, hypocenter | C52 | C4×C361 |
| Frattini | C19 | C19×#1044 |
| Fitting | C52×C361 | C4 |
| socle | C52×C19 | C4×C19 |
| prime radical, cosocle | C19×C5⋊D5 | C2×C19 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C361 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3610 |
3610 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36100, 23);