Finite Group Databasebeta

← Prev (#50303692) Next (#50303694) →

C3×C13×C7⋊Dic35 #50303693

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

Aliases

direct productC3×C13×C7⋊Dic35

Splittings

derived, HallC5×C72 ⋊ C3×C4×C13
HallC3×C5×C72×C13 ⋊ C4
HallC5×C72×C13 ⋊ C3×C4
HallC3×C72×C13 ⋊ Dic5
HallC3×C5×C72 ⋊ C4×C13
HallC72×C13 ⋊ C3×Dic5
HallC3×C5×C13 ⋊ C7⋊Dic7
HallC3×C72 ⋊ C13×Dic5
HallC5×C13 ⋊ C3×C7⋊Dic7
SylowC72 ⋊ C3×C13×Dic5
HallC3×C5 ⋊ C13×C7⋊Dic7
SylowC5 ⋊ C3×C13×C7⋊Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13C5⋊(C7⋊D7)
commutator, hypocenterC5×C72C3×C4×C13
FrattiniC2C3×C13×C5⋊(C7⋊D7)
Fitting, socle, prime radicalC2×C3×C5×C72×C13C2
cosocleC2×C5×C72C2×C3×C13
LCSG ▷ C5×C72
UCSC1 ◁ C2×C3×C13

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 38220

Conjugacy classes & character table

9672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 379);