Finite Group Databasebeta

← Prev (#28414739) Next (#28414741) →

C5×C19×Dic13⋊C3 #28414740

order14820
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC5×C19×Dic13⋊C3
unambiguous semidirect productDic13⋊(C3×C5×C19)
unambiguous semidirect product(C5×Dic13)⋊(C3×C19)

Splittings

derived, SylowC13 ⋊ C3×C4×C5×C19
HallC5×C19×Dic13 ⋊ C3
HallC5×C19×C13⋊C3 ⋊ C4
HallC5×C13×C19 ⋊ C3×C4
HallC19×Dic13 ⋊ C3×C5
HallC19×C13⋊C3 ⋊ C4×C5
HallC5×Dic13 ⋊ C3×C19
HallC13×C19 ⋊ C3×C4×C5
HallC5×C13⋊C3 ⋊ C4×C19
HallC5×C13 ⋊ C3×C4×C19
HallDic13 ⋊ C3×C5×C19
HallC13⋊C3 ⋊ C4×C5×C19

Subgroups

subgroupG/H
center, hypercenterC2×C5×C19D13⋊C3
commutator, hypocenterC13C3×C4×C5×C19
FrattiniC2C5×C19×D13⋊C3
Fitting, socleC2×C5×C13×C19C2×C3
prime radicalC2×C5×C19×C13⋊C3C2
cosocleC2×C13C2×C3×C5×C19
LCSG ▷ C13
UCSC1 ◁ C2×C5×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4940

Conjugacy classes & character table

1520 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 26);