Finite Group DatabasebetaFinite Group Databasebeta| order | 38220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10587717⋊D35 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C13 | C22×C3 |
| LCS | G ▷ C5×C72×C13 | |
| UCS | C1 | |
200 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 39 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:
2^2,3,5,7^2,13|g^a=g^12,d^b=d^4,e^b=e^6,f^b=f^6,e^c=e^2,g^c=g^9432 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38220, 699);