Finite Group Databasebeta

← Prev (#50304337) Next (#50304339) →

C3×C5×#14579331 #50304338

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

Aliases

direct productC3×C5×#14579331

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C4
derived, HallC72×C13 ⋊ C3×C4×C5
HallC5×C72×C13 ⋊ C3×C4
HallC3×C72×C13 ⋊ C4×C5
HallC3×C5×C72 ⋊ Dic13
HallC5×C72 ⋊ C3×Dic13
HallC3×C5×C13 ⋊ #5997
HallC3×C72 ⋊ C5×Dic13
HallC5×C13 ⋊ C3×#5997
SylowC72 ⋊ C3×C5×Dic13
HallC3×C13 ⋊ C5×#5997
SylowC13 ⋊ C3×C5×#5997

Subgroups

subgroupG/H
center, hypercenterC3×C5#14579331
commutator, hypocenterC72×C13C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C72×C13C4
prime radicalC3×C5×C13×C7⋊D7C2
cosocleC13×C7⋊D7C2×C3×C5
LCSG ▷ C72×C13
UCSC1 ◁ C3×C5

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

2580 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1024);