Finite Group Databasebeta

← Prev (#30627755) Next (#30627757) →

C4×C13×C43⋊C7 #30627756

order15652
isoclinismisoclinic class of C43⋊C7
automorphism?
homologyAbelianization (H1) = C4×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13×C43⋊C7
unambiguous semidirect product(C4×C43)⋊(C7×C13)
unambiguous semidirect product(C4×C13×C43)⋊C7

Splittings

Fitting, HallC4×C13×C43 ⋊ C7
derived, SylowC43 ⋊ C4×C7×C13
HallC13×C43 ⋊ C4×C7
HallC4×C43 ⋊ C7×C13

Subgroups

subgroupG/H
center, hypercenterC4×C13C43⋊C7
commutator, hypocenterC43C4×C7×C13
FrattiniC2C2×C13×C43⋊C7
FittingC4×C13×C43C7
socleC2×C13×C43C2×C7
prime radicalC2×C13×C43⋊C7C2
cosocleC2×C43C2×C7×C13
LCSG ▷ C43
UCSC1 ◁ C4×C13

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2236

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15652, 2);