Finite Group Databasebeta

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C3×D3×C7×C41⋊C5 #38788946

order25830
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×D3×C7×C41⋊C5
unambiguous semidirect productC3⋊(C2×C3×C7×C41⋊C5)
unambiguous semidirect product(D3×C41)⋊(C3×C5×C7)
unambiguous semidirect product(C3×D3×C41)⋊(C5×C7)
unambiguous semidirect product(C3×D3×C7×C41)⋊C5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C7D3×C41⋊C5
commutator, cosocle, hypocenterC3×C41C2×C3×C5×C7
FrattiniC1G
Fitting, socleC32×C7×C41C2×C5
LCSG ▷ C3×C41
UCSC1 ◁ C3×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1722

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 50);