Finite Group DatabasebetaFinite Group Databasebeta| order | 38220 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#19129750 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #19129750 |
| commutator, hypocenter | C5×C7×C13 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C13 | C3×C4 |
| prime radical | C72×D5×C13⋊C3 | C2 |
| cosocle | C7×D5×C13 | C2×C3×C7 |
| LCS | G ▷ C5×C7×C13 | |
| UCS | C1 ◁ C7 | |
144 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 910 |
749 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38220, 572);