Finite Group DatabasebetaFinite Group Databasebeta| order | 38220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×C13×C5⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (C2×C5)⋊(C7×C13×AGL(1,𝔽7)) |
| unambiguous semidirect product | (C2×ΓL(1,𝔽8))⋊(C7×D5×C13) |
| unambiguous semidirect product | (C2×D35)⋊(C3×C7×C13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C13 | C5⋊AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C5×C7 | C22×C3×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C72×C13 | C2×C3 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C2×C7×C13 | |
168 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5460 |
3094 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38220, 968);