Finite Group DatabasebetaFinite Group Databasebeta| order | 38220 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| direct product | C13⋊C3×C7⋊(C7⋊AGL(1,𝔽5)) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C72×C13 | C3×C4 |
| prime radical | C72×D5×C13⋊C3 | C2 |
| cosocle | C72×D5×C13 | C2×C3 |
| LCS | G ▷ C5×C72×C13 | |
| UCS | C1 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3185 |
707 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38220, 641);