Finite Group DatabasebetaFinite Group Databasebeta| order | 38220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C13×C5⋊(ΓL(1,𝔽8)⋊D7) |
| unambiguous semidirect product | (C2×C5)⋊(C13×ΓL(1,𝔽8)⋊D7) |
| unambiguous semidirect product | (C2×ΓL(1,𝔽8))⋊(C13×D35) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | C5⋊(ΓL(1,𝔽8)⋊D7) |
| commutator, cosocle, hypocenter | C5×C72 | C22×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C72×C13 | C2×C3 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C2×C13 | |
200 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2730 |
2392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38220, 974);