Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | C23×#90646⋊C2 |
| unambiguous semidirect product | #90646⋊(C2×C23) |
| unambiguous semidirect product | ((C5⋊D5)⋊C9)⋊(C2×C23) |
| derived, Hall | C52⋊C9 ⋊ C22×C23 |
| Hall | C23×C52⋊C9 ⋊ C22 |
| Hall | C52×C23 ⋊ C2×D9 |
| Sylow | C52 ⋊ C2×D9×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #90646⋊C2 |
| commutator, cosocle, hypocenter | C52⋊C9 | C22×C23 |
| Frattini | C3 | C23×#3874⋊C2 |
| Fitting, socle | C3×C52×C23 | C2×D3 |
| LCS | G ▷ C52⋊C9 | |
| UCS | C1 ◁ C23 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1035 |
552 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 108);