Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×C5×D115 |
| unambiguous semidirect product | (C2×C5)⋊(C32×C5×D23) |
| unambiguous semidirect product | (C2×C23)⋊(C32×C5×D5) |
| Fitting, socle | C2×C32×C52×C23 ⋊ C2 |
| derived | C5×C23 ⋊ C22×C32×C5 |
| Hall | C32×C52×C23 ⋊ C22 |
| Hall | C52×C23 ⋊ C22×C32 |
| Hall | C32×C52 ⋊ C2×D23 |
| Hall | C32×C23 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ C2×C32×D23 |
| Sylow | C23 ⋊ C2×C32×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C5 | D115 |
| commutator, cosocle, hypocenter | C5×C23 | C22×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C52×C23 | C2 |
| LCS | G ▷ C5×C23 | |
| UCS | C1 ◁ C2×C32×C5 | |
288 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4140 |
5310 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 357);