Finite Group Databasebeta

C4×C13×C13⋊C3 #14523134

order2028
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13×C13⋊C3
unambiguous semidirect product(C4×C13)⋊(C3×C13)

Splittings

Fitting, HallC4×C132 ⋊ C3
derivedC13 ⋊ C3×C4×C13
SylowC132 ⋊ C3×C4

Subgroups

subgroupG/H
center, hypercenterC4×C13C13⋊C3
commutator, hypocenterC13C3×C4×C13
FrattiniC2C2×C13×C13⋊C3
FittingC4×C132C3
socleC2×C132C2×C3
prime radicalC2×C13×C13⋊C3C2
cosocleC2×C13C2×C3×C13
LCSG ▷ C13
UCSC1 ◁ C4×C13

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 156

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC13×#11763961, C13×#11763962, C13×Dic7×C13⋊C3, …
maximal normal subgroup ofC4×C7×C13×C13⋊C3, C4×C11×C13×C13⋊C3, C4×C13×C17×C13⋊C3, …
maximal quotient ofC13×#11763961, C13×#11763962, C13×Dic7×C13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2028, 28);