Finite Group DatabasebetaFinite Group Databasebeta| order | 19220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | #18012458 ⋊ C4 |
| Sylow | C312 ⋊ Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #23751208 |
| commutator, hypocenter | #18012458 | C4 |
| Fitting, socle | C2×C312 | D5 |
| prime radical, cosocle | C2×#18012458 | C2 |
| LCS | G ▷ #18012458 | |
| UCS | C1 ◁ C2 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 124 |
Polycyclic presentation:
2,5,31^2,2|a^2=e,b^a=b^4,c^a=d,d^a=c,c^b=c^2,d^b=d^16290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19220, 17);