Finite Group Databasebeta

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D3×C7×C13×C11⋊C5 #44473264

order30030
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productD3×C7×C13×C11⋊C5
unambiguous semidirect productC3⋊(C2×C7×C13×C11⋊C5)
unambiguous semidirect product(D3×C11)⋊(C5×C7×C13)
unambiguous semidirect product(D3×C7×C11)⋊(C5×C13)
unambiguous semidirect product(D3×C11×C13)⋊(C5×C7)
unambiguous semidirect product(D3×C7×C11×C13)⋊C5

Splittings

Fitting, socle, HallC3×C7×C11×C13 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C5×C7×C13
HallC3×C7×C13×C11⋊C5 ⋊ C2
HallD3×C7×C11×C13 ⋊ C5
HallC3×C13×C11⋊C5 ⋊ C2×C7
HallC3×C7×C11⋊C5 ⋊ C2×C13
HallC7×C11×C13 ⋊ C5×D3
HallD3×C11×C13 ⋊ C5×C7
HallD3×C7×C11 ⋊ C5×C13
HallC3×C11×C13 ⋊ C2×C5×C7
HallC3×C7×C13 ⋊ C2×C11⋊C5
HallC3×C7×C11 ⋊ C2×C5×C13
HallC3×C11⋊C5 ⋊ C2×C7×C13
HallC11×C13 ⋊ C5×D3×C7
HallC7×C11 ⋊ C5×D3×C13
HallD3×C11 ⋊ C5×C7×C13
HallC3×C13 ⋊ C2×C7×C11⋊C5
HallC3×C7 ⋊ C2×C13×C11⋊C5
SylowC11 ⋊ C5×D3×C7×C13
SylowC3 ⋊ C2×C7×C13×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC7×C13D3×C11⋊C5
commutator, cosocle, hypocenterC3×C11C2×C5×C7×C13
FrattiniC1G
Fitting, socleC3×C7×C11×C13C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C7×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3003

Conjugacy classes & character table

1911 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 49);