Finite Group Databasebeta

← Prev (#26046184) Next (#26046186) →

C5×C3⋊#11716328 #26046185

order11970
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊#11716328
unambiguous semidirect productC3⋊(C5×#11716328)

Splittings

Fitting, socleC3×C5×C7×C19 ⋊ C2×C3
derivedC3×C7×C19 ⋊ C2×C3×C5
HallC3×C5×#87705 ⋊ C2
HallC3×#87705 ⋊ C2×C5
HallC5×C7×C19 ⋊ C3×D3
HallC7×C19 ⋊ C3×C5×D3
HallC5×C19 ⋊ C3⋊AGL(1,𝔽7)
HallC5×C7 ⋊ C3⋊(D19⋊C3)
SylowC19 ⋊ C5×C3⋊AGL(1,𝔽7)
SylowC7 ⋊ C5×C3⋊(D19⋊C3)

Subgroups

subgroupG/H
center, hypercenterC5C3⋊#11716328
commutator, cosocle, hypocenterC3×C7×C19C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C19C2×C3
LCSG ▷ C3×C7×C19
UCSC1 ◁ C5

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

375 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#11716322⋊D3, C5×#11716326⋊D3, C5×D3×#11716328, …
maximal normal subgroup ofC5×#11716322⋊D3, C5×#11716326⋊D3, C5×D3×#11716328, …
maximal quotient ofC5×C3⋊#13097589, C2×C5×C3⋊#11716328

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 114);