Finite Group DatabasebetaFinite Group Databasebeta| order | 19220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C31 |
No aliases for this group.
| Fitting, socle, Sylow | C312 ⋊ Dic5 |
| derived, Hall | #18012458 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | #18012458 | C4 |
| Fitting, socle | C312 | Dic5 |
| prime radical, cosocle | #23751218 | C2 |
| LCS | G ▷ #18012458 | |
| UCS | C1 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 62 |
Polycyclic presentation:
2^2,5,31^2|a^2=b,c^a=c^4,d^a=d^27e^21,e^a=d^11e^4,d^b=d^30,e^b=e^30,d^c=d^8e^24,e^c=e^456 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19220, 39);