Finite Group DatabasebetaFinite Group Databasebeta| order | 38220 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
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⋊((C13⋊C3)⋊(C7⋊D7)) | C2 |
| cosocle | C5⋊(C7⋊D91) | 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^2,e^a=e^3f^5,f^a=e^5f^4,g^a=g^5,g^b=g^3,d^c=d^4,e^c=e^6,f^c=f^6,g^c=g^12440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38220, 494);