Finite Group DatabasebetaFinite Group Databasebeta| order | 26820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×D5×D149 |
| unambiguous semidirect product | (D5×C149)⋊(C2×C32) |
| unambiguous semidirect product | (C5×D149)⋊(C2×C32) |
| unambiguous semidirect product | D745⋊(C2×C32) |
| Fitting, socle, Hall | C32×C5×C149 ⋊ C22 |
| derived, Hall | C5×C149 ⋊ C22×C32 |
| Hall | C32×C149 ⋊ C2×D5 |
| Sylow | C149 ⋊ C2×C32×D5 |
| Hall | C32×C5 ⋊ C2×D149 |
| Sylow | C5 ⋊ C2×C32×D149 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D5×D149 |
| commutator, cosocle, hypocenter | C5×C149 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C149 | C22 |
| LCS | G ▷ C5×C149 | |
| UCS | C1 ◁ C32 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6705 |
2736 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26820, 66);