Finite Group DatabasebetaFinite Group Databasebeta| order | 21700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2 |
| direct product | C5×C7×D5×D31 |
| Fitting, socle, Hall | C52×C7×C31 ⋊ C22 |
| derived | C5×C31 ⋊ C22×C5×C7 |
| Hall | C52×C31 ⋊ C22×C7 |
| Hall | C7×C31 ⋊ C2×C5×D5 |
| Hall | C52×C7 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×C5×C7×D5 |
| Sylow | C52 ⋊ C2×C7×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | D5×D31 |
| commutator, cosocle, hypocenter | C5×C31 | C22×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C31 | C22 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 ◁ C5×C7 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2170 |
2380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21700, 78);