Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C23 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C3×C23×C3⋊(C5⋊D5) |
| unambiguous semidirect product | (C2×C3)⋊(C3×C23×C5⋊D5) |
| unambiguous semidirect product | (C2×C5)⋊(C3×C23×D15) |
| Fitting, socle | C2×C32×C52×C23 ⋊ C2 |
| derived | C3×C52 ⋊ C22×C3×C23 |
| Hall | C32×C52×C23 ⋊ C22 |
| Hall | C52×C23 ⋊ C2×C3×D3 |
| Hall | C32×C52 ⋊ C22×C23 |
| Hall | C32×C23 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ C2×C3×D3×C23 |
| Sylow | C32 ⋊ C2×C23×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C23 | C3⋊(C5⋊D5) |
| commutator, cosocle, hypocenter | C3×C52 | C22×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C52×C23 | C2 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2×C3×C23 | |
352 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6900 |
5382 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 364);