Finite Group DatabasebetaFinite Group Databasebeta| order | 21700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C31 · Schur multiplier (H2) = C2 |
| direct product | C7×D52×C31 |
| unambiguous semidirect product | (C5×D5)⋊(C2×C7×C31) |
| unambiguous semidirect product | (C5⋊D5)⋊(C2×C7×C31) |
| Fitting, socle, Hall | C52×C7×C31 ⋊ C22 |
| derived, Sylow | C52 ⋊ C22×C7×C31 |
| Hall | C52×C31 ⋊ C22×C7 |
| Hall | C52×C7 ⋊ C22×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C31 | D52 |
| commutator, cosocle, hypocenter | C52 | C22×C7×C31 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C31 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C7×C31 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2170 |
3472 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21700, 92);