Finite Group DatabasebetaFinite Group Databasebeta| order | 38220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C5×C13×#3862 | C4 |
| Fitting, socle | C5×C72×C13 | Dic3 |
| prime radical, cosocle | C5⋊#16838454 | C2 |
| LCS | G ▷ C5×C13×#3862 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 910 |
Polycyclic presentation:
2^2,3,5,13,7^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^5,f^a=f^5g^2,g^a=fg^2,d^b=d^4,e^b=e^12,f^b=f^6,g^b=g^6,f^c=f^4g^4,g^c=g^2314 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38220, 503);