Finite Group Databasebeta

← Prev (#36319573) Next (#36319575) →

C4×C13⋊C3×C137 #36319574

order21372
automorphism?
homologyAbelianization (H1) = C3×C4×C137 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13⋊C3×C137
unambiguous semidirect product(C4×C13)⋊(C3×C137)
unambiguous semidirect product(C4×C13×C137)⋊C3

Splittings

Fitting, HallC4×C13×C137 ⋊ C3
derived, SylowC13 ⋊ C3×C4×C137
HallC13×C137 ⋊ C3×C4
HallC4×C13 ⋊ C3×C137

Subgroups

subgroupG/H
center, hypercenterC4×C137C13⋊C3
commutator, hypocenterC13C3×C4×C137
FrattiniC2C2×C13⋊C3×C137
FittingC4×C13×C137C3
socleC2×C13×C137C2×C3
prime radicalC2×C13⋊C3×C137C2
cosocleC2×C13C2×C3×C137
LCSG ▷ C13
UCSC1 ◁ C4×C137

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7124

Conjugacy classes & character table

3836 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21372, 2);