Finite Group DatabasebetaFinite Group Databasebeta| order | 38220 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C7⋊#63118) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C72×C13 | C3×C4 |
| prime radical | C5×C7×ΓL(1,𝔽8)×D13 | C2 |
| cosocle | C5×C72×D13 | C2×C3 |
| LCS | G ▷ C5×C72×C13 | |
| UCS | C1 | |
120 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1365 |
Polycyclic presentation:
2,3,2,5,7^2,13|a^2=c,d^a=d^4,e^a=e^6,f^a=f^6,g^a=g^5,e^b=e^2,g^c=g^12709 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38220, 700);