Finite Group Databasebeta

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D3×C7×D5×C11 #17987708

order4620
automorphism?
homologyAbelianization (H1) = C22×C7×C11 · Schur multiplier (H2) = C2

Aliases

direct productD3×C7×D5×C11
unambiguous semidirect product(C5×D3)⋊(C2×C7×C11)
unambiguous semidirect product(C3×D5)⋊(C2×C7×C11)
unambiguous semidirect productD15⋊(C2×C7×C11)

Splittings

Fitting, socle, HallC3×C5×C7×C11 ⋊ C22
derived, HallC3×C5 ⋊ C22×C7×C11
HallC5×C7×C11 ⋊ C2×D3
HallC3×C7×C11 ⋊ C2×D5
HallC3×C5×C11 ⋊ C22×C7
HallC3×C5×C7 ⋊ C22×C11
HallC5×C11 ⋊ C2×D3×C7
HallC5×C7 ⋊ C2×D3×C11
HallC3×C11 ⋊ C2×C7×D5
HallC3×C7 ⋊ C2×D5×C11
SylowC5 ⋊ C2×D3×C7×C11
SylowC3 ⋊ C2×C7×D5×C11

Subgroups

subgroupG/H
center, hypercenterC7×C11D3×D5
commutator, cosocle, hypocenterC3×C5C22×C7×C11
FrattiniC1G
Fitting, socleC3×C5×C7×C11C22
LCSG ▷ C3×C5
UCSC1 ◁ C7×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 1155

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×D5×C11×D9, D3×D5×C11×ΓL(1,𝔽8), C3×D3×C7×D5×C11, …
maximal normal subgroup ofD3×D5×C11×ΓL(1,𝔽8), C3×D3×C7×D5×C11, D3×C7×D5×C11⋊C5, …
maximal quotient ofC7×D5×C11×D9, C3×D3×C7×D5×C11, C7×D5×C11×C3⋊D3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4620, 105);