Finite Group Databasebeta

← Prev (#28356660) Next (#28356662) →

C19⋊C3×3−1+4 #28356661

order13851
automorphism?
homologyAbelianization (H1) = C35 · Schur multiplier (H2) = C39

Aliases

direct productC19⋊C3×3−1+4

Splittings

FittingC19×3−1+4 ⋊ C3
SylowC19 ⋊ C3×3−1+4

Subgroups

subgroupG/H
center, FrattiniC3C34×C19⋊C3
commutator, socle, cosocleC3×C19C35
FittingC19×3−1+4C3
prime radicalC3×H(3,𝔽3)×C19⋊C3C3
hypercenter3−1+4C19⋊C3
hypocenterC19C3×3−1+4
LCSG ▷ C3×C19 ▷ C19
UCSC1 ◁ C3 ◁ 3−1+4

5588 conjugacy classes of subgroups; only the 2881 normal subgroups are shown.

normal subgroups only

This group has 5588 conjugacy classes of subgroups — too many to draw. Only its 2881 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 513

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 4025);