Finite Group Databasebeta

← Prev (#34062097) Next (#34062099) →

C5×#16838474 #34062098

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#16838474

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C2×C3
derived, HallC72×C13 ⋊ C2×C3×C5
HallC5×#14274262 ⋊ C2
HallC5×C72×D13 ⋊ C3
Hall#14274262 ⋊ C2×C5
HallC72×D13 ⋊ C3×C5
HallC5×C72 ⋊ D13⋊C3
HallC5×D13 ⋊ #3861
HallC5×C13 ⋊ C2×#3861
SylowC72 ⋊ C5×D13⋊C3
HallD13 ⋊ C5×#3861
SylowC13 ⋊ C2×C5×#3861

Subgroups

subgroupG/H
center, hypercenterC5#16838474
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

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

Relationships

maximal subgroup ofC5×#21439654, C5×#21439598, C5×#21439600, …
maximal normal subgroup ofC5×#21439654, C5×#21439598, C5×#21439600, …
maximal quotient ofC5×#21439550, C2×C5×#16838474

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 91);