Finite Group DatabasebetaFinite Group Databasebeta| order | 35700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C52×D357 |
| unambiguous semidirect product | (C2×C3)⋊(C52×D119) |
| unambiguous semidirect product | (C2×C7)⋊(C52×D51) |
| unambiguous semidirect product | (C2×C17)⋊(C52×D21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | D357 |
| commutator, cosocle, hypocenter | C3×C7×C17 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52×C7×C17 | C2 |
| LCS | G ▷ C3×C7×C17 | |
| UCS | C1 ◁ C2×C52 | |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17850 |
9000 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35700, 528);