Finite Group Databasebeta

← Prev (#50304364) Next (#50304366) →

C3×#27164969 #50304365

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

Aliases

direct productC3×#27164969

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C4
derived, HallC5×C72×C13 ⋊ C3×C4
HallC3×C72×C13 ⋊ Dic5
HallC3×C5×C72 ⋊ Dic13
HallC72×C13 ⋊ C3×Dic5
HallC5×C72 ⋊ C3×Dic13
HallC3×C5×C13 ⋊ #5997
HallC3×C72 ⋊ Dic65
HallC5×C13 ⋊ C3×#5997
SylowC72 ⋊ C3×Dic65
HallC3×C13 ⋊ #11758267
HallC3×C5 ⋊ #14579331
SylowC13 ⋊ C3×#11758267
SylowC5 ⋊ C3×#14579331

Subgroups

subgroupG/H
center, hypercenterC3#27164969
commutator, hypocenterC5×C72×C13C3×C4
FrattiniC1G
Fitting, socleC3×C5×C72×C13C4
prime radicalC3×C5×C13×C7⋊D7C2
cosocleC5×C13×C7⋊D7C2×C3
LCSG ▷ C5×C72×C13
UCSC1 ◁ C3

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

2544 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1051);