Finite Group DatabasebetaFinite Group Databasebeta| order | 21300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C71 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C3×C5⋊D5×C71 |
| unambiguous semidirect product | (C2×C5)⋊(C3×D5×C71) |
| Fitting, socle | C2×C3×C52×C71 ⋊ C2 |
| derived, Sylow | C52 ⋊ C22×C3×C71 |
| Hall | C3×C52×C71 ⋊ C22 |
| Hall | C52×C71 ⋊ C22×C3 |
| Hall | C3×C52 ⋊ C22×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C71 | C5⋊D5 |
| commutator, cosocle, hypocenter | C52 | C22×C3×C71 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52×C71 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C3×C71 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10650 |
5964 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21300, 145);