Finite Group Databasebeta

← Prev (#35208803) Next (#35208805) →

C7×#15688279 #35208804

order20748
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×#15688279

Splittings

derived, HallC13×C19 ⋊ C3×C4×C7
HallC7×C13×Dic19 ⋊ C3
HallC7×#10625202 ⋊ C4
HallC7×C13×C19 ⋊ C3×C4
HallC13×Dic19 ⋊ C3×C7
Hall#10625202 ⋊ C4×C7
HallC7×Dic19 ⋊ C13⋊C3
HallC7×C19 ⋊ C4×C13⋊C3
HallC7×C13 ⋊ (C19⋊C3)⋊C4
HallDic19 ⋊ C7×C13⋊C3
SylowC19 ⋊ C4×C7×C13⋊C3
SylowC13 ⋊ C7×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C7#13093360
commutator, hypocenterC13×C19C3×C4×C7
FrattiniC2C7×#13093360
Fitting, socleC2×C7×C13×C19C2×C3
prime radicalC2×C7×#10625202C2
cosocleC2×C13×C19C2×C3×C7
LCSG ▷ C13×C19
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6916

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 32);