Finite Group Databasebeta

D19×#1303 #18072825

order4864
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productD19×#1303

Splittings

FittingC19×#1303 ⋊ C2
SylowC19 ⋊ C2×#1303

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D19
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC19×#1303C2
socleC22×C19C2×#95
prime radicalC23×D19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1303D19
hypocenterC19C2×#1303
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 608

Conjugacy classes & character table

418 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 59854);