Finite Group DatabasebetaFinite Group Databasebeta| order | 36100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C361 · Schur multiplier (H2) = C5 |
| direct product | #1039×C361 |
| derived, Sylow | C52 ⋊ C4×C361 |
| Hall | C52×C361 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C361 | C5⋊D5 |
| commutator, hypocenter | C52 | C4×C361 |
| Frattini | C2×C19 | C19×C5⋊D5 |
| Fitting | C2×C52×C361 | C2 |
| socle, prime radical, cosocle | C2×C52×C19 | C2×C19 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C361 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36100 |
10108 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36100, 16);