Finite Group DatabasebetaFinite Group Databasebeta| order | 38220 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C72×C13 | C3×C4 |
| prime radical | C5×#16838449 | C2 |
| cosocle | C5×C13×C7⋊D7 | C2×C3 |
| LCS | G ▷ C5×C72×C13 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 910 |
Polycyclic presentation:
2,3,2,5,7^2,13|a^2=c,d^a=d^4,e^a=e^4f^4,f^a=ef^3,e^b=e^2,f^b=f^2,g^b=g^9,e^c=e^6,f^c=f^6316 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38220, 661);