Finite Group Databasebeta

← Prev (#34062108) Next (#34062110) →

C5×C13⋊C3×C7⋊D7 #34062109

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C7

Aliases

direct productC5×C13⋊C3×C7⋊D7

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C2×C3
derived, HallC72×C13 ⋊ C2×C3×C5
HallC5×C72×C13⋊C3 ⋊ C2
HallC5×C13×C7⋊D7 ⋊ C3
HallC72×C13⋊C3 ⋊ C2×C5
HallC13×C7⋊D7 ⋊ C3×C5
HallC5×C72 ⋊ C2×C13⋊C3
HallC5×C13 ⋊ C3×C7⋊D7
SylowC72 ⋊ C2×C5×C13⋊C3
SylowC13 ⋊ C3×C5×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC5C13⋊C3×C7⋊D7
commutator, cosocle, hypocenterC72×C13C2×C3×C5
FrattiniC1G
Fitting, socleC5×C72×C13C2×C3
LCSG ▷ C72×C13
UCSC1 ◁ C5

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3185

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#21439687, C5×C13⋊C3×#5997, C5×((C13⋊C3)⋊D7)⋊D7, …
maximal normal subgroup ofC5×#21439687, C5×C13⋊C3×#5997, C5×((C13⋊C3)⋊D7)⋊D7, …
maximal quotient ofC5×C13⋊C3×C7⋊Dic7, C2×C5×C13⋊C3×C7⋊D7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 102);