Finite Group Databasebeta

← Prev (#50303671) Next (#50303673) →

C4×C5×C13×#3862 #50303672

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C13 · Schur multiplier (H2) = C7

Aliases

direct productC4×C5×C13×#3862

Splittings

Fitting, HallC4×C5×C72×C13 ⋊ C3
derived, SylowC72 ⋊ C3×C4×C5×C13
HallC5×C72×C13 ⋊ C3×C4
HallC4×C72×C13 ⋊ C3×C5
HallC4×C5×C72 ⋊ C3×C13
HallC72×C13 ⋊ C3×C4×C5
HallC5×C72 ⋊ C3×C4×C13
HallC4×C72 ⋊ C3×C5×C13

Subgroups

subgroupG/H
center, hypercenterC4×C5×C13#3862
commutator, hypocenterC72C3×C4×C5×C13
FrattiniC2C2×C5×C13×#3862
FittingC4×C5×C72×C13C3
socleC2×C5×C72×C13C2×C3
prime radicalC2×C5×C13×#3862C2
cosocleC2×C72C2×C3×C5×C13
LCSG ▷ C72
UCSC1 ◁ C4×C5×C13

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5460

Conjugacy classes & character table

4940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 358);