Finite Group DatabasebetaFinite Group Databasebeta| order | 35700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×C17⋊#3874 |
| unambiguous semidirect product | (C2×C17)⋊(C7×#3874) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | C17⋊#3874 |
| commutator, cosocle, hypocenter | C17×C52⋊C3 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C7×C17 | D3 |
| LCS | G ▷ C17×C52⋊C3 | |
| UCS | C1 ◁ C2×C7 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3570 |
1414 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35700, 314);