Finite Group DatabasebetaFinite Group Databasebeta| order | 36100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C19 |
| direct product | C2×C19⋊D475 |
| unambiguous semidirect product | (C2×C19)⋊D475 |
| unambiguous semidirect product | (C2×C25)⋊(C19⋊D19) |
| Fitting | C2×C192×C25 ⋊ C2 |
| derived, Hall | C192×C25 ⋊ C22 |
| Sylow | C192 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×C19⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C19⋊D475 |
| commutator, cosocle, hypocenter | C192×C25 | C22 |
| Frattini | C5 | C2×C5⋊(C19⋊D19) |
| Fitting | C2×C192×C25 | C2 |
| socle | C2×C5×C192 | D5 |
| LCS | G ▷ C192×C25 | |
| UCS | C1 ◁ C2 | |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18050 |
9028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36100, 64);