Finite Group Databasebeta

← Prev (#34062087) Next (#34062089) →

C5×#16838464 #34062088

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

Aliases

direct productC5×#16838464

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C2×C3
derived, HallC72×C13 ⋊ C2×C3×C5
HallC5×C13⋊#3862 ⋊ C2
HallC5×C7×C13×D7 ⋊ C3
HallC13⋊#3862 ⋊ C2×C5
HallC7×C13×D7 ⋊ C3×C5
HallC5×C7×D7 ⋊ C13⋊C3
HallC5×C72 ⋊ C2×C13⋊C3
HallC7×D7 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ #64422
SylowC72 ⋊ C2×C5×C13⋊C3
SylowC13 ⋊ C5×#64422

Subgroups

subgroupG/H
center, hypercenterC5#16838464
commutator, cosocle, hypocenterC72×C13C2×C3×C5
FrattiniC1G
Fitting, socleC5×C72×C13C2×C3
LCSG ▷ C72×C13
UCSC1 ◁ C5

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#21439631, C5×#21439617, C5×#21439620, …
maximal normal subgroup ofC5×#21439631, C5×#21439617, C5×#21439620, …
maximal quotient ofC5×#21439540, C2×C5×#16838464

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 81);