Finite Group Databasebeta

← Prev (#38788947) Next (#38788949) →

C3×D21×C41⋊C5 #38788948

order25830
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×D21×C41⋊C5
unambiguous semidirect productC3⋊(C3×D7×C41⋊C5)
unambiguous semidirect product(C3×C41×D21)⋊C5

Splittings

Fitting, socle, HallC32×C7×C41 ⋊ C2×C5
derivedC3×C7×C41 ⋊ C2×C3×C5
HallC32×C7×C41⋊C5 ⋊ C2
HallC3×C41×D21 ⋊ C5
HallC32×C41⋊C5 ⋊ D7
HallC7×C41⋊C5 ⋊ C3×D3
HallC32×C41 ⋊ C5×D7
HallC7×C41 ⋊ C3×C5×D3
HallC32×C7 ⋊ C2×C41⋊C5
SylowC41 ⋊ C3×C5×D21
SylowC32 ⋊ D7×C41⋊C5
SylowC7 ⋊ C3×D3×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC3D21×C41⋊C5
commutator, cosocle, hypocenterC3×C7×C41C2×C3×C5
FrattiniC1G
Fitting, socleC32×C7×C41C2×C5
LCSG ▷ C3×C7×C41
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1722

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 52);