Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | C23×D152 |
| Fitting, socle, Hall | C32×C52×C23 ⋊ C22 |
| derived, Hall | C32×C52 ⋊ C22×C23 |
| Hall | C52×C23 ⋊ D32 |
| Hall | C32×C23 ⋊ D52 |
| Sylow | C52 ⋊ D32×C23 |
| Sylow | C32 ⋊ D52×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D152 |
| commutator, cosocle, hypocenter | C32×C52 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C23 | C22 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C23 | |
224 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 690 |
1863 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 312);