Finite Group Databasebeta

← Prev (#34086251) Next (#34086253) →

C5×C7×C3⋊(D31⋊C3) #34086252

order19530
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C3⋊(D31⋊C3)
unambiguous semidirect productC3⋊(C5×C7×D31⋊C3)
unambiguous semidirect product(C5×D93)⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C31 ⋊ C2×C3
derivedC3×C31 ⋊ C2×C3×C5×C7
HallC3×C5×C7×C31⋊C3 ⋊ C2
HallC3×C7×C31⋊C3 ⋊ C2×C5
HallC3×C5×C31⋊C3 ⋊ C2×C7
HallC5×C7×C31 ⋊ C3×D3
HallC3×C31⋊C3 ⋊ C2×C5×C7
HallC7×C31 ⋊ C3×C5×D3
HallC5×C31 ⋊ C3×D3×C7
SylowC31 ⋊ C3×C5×D3×C7

Subgroups

subgroupG/H
center, hypercenterC5×C7C3⋊(D31⋊C3)
commutator, cosocle, hypocenterC3×C31C2×C3×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C31C2×C3
LCSG ▷ C3×C31
UCSC1 ◁ C5×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3255

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 157);