Finite Group DatabasebetaFinite Group Databasebeta| order | 19220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #23751208⋊C2 |
| Fitting, socle, Sylow | C312 ⋊ C2×D5 |
| derived, Hall | #18012458 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #18012458 | C22 |
| Fitting, socle | C312 | C2×D5 |
| LCS | G ▷ #18012458 | |
| UCS | C1 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 62 |
Polycyclic presentation:
2^2,5,31^2|d^a=d^30,e^a=e^30,c^b=c^4,d^b=e^23,e^b=d^27,d^c=d^8,e^c=e^4101 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19220, 38);