Finite Group Databasebeta

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D11×D105 #17987703

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

Aliases

direct productD11×D105
unambiguous semidirect product(C3×D11)⋊D35
unambiguous semidirect product(C5×D11)⋊D21
unambiguous semidirect product(C7×D11)⋊D15

Splittings

Fitting, socle, derived, HallC3×C5×C7×C11 ⋊ C22
HallC5×C7×C11 ⋊ C2×D3
HallC3×C7×C11 ⋊ C2×D5
HallC3×C5×C11 ⋊ C2×D7
HallC3×C5×C7 ⋊ C2×D11
HallC7×C11 ⋊ C2×D15
HallC5×C11 ⋊ C2×D21
HallC5×C7 ⋊ D3×D11
HallC3×C11 ⋊ C2×D35
HallC3×C7 ⋊ D5×D11
HallC3×C5 ⋊ D7×D11
SylowC11 ⋊ C2×D105
SylowC7 ⋊ D11×D15
SylowC5 ⋊ D11×D21
SylowC3 ⋊ D11×D35

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C11C22
LCSG ▷ C3×C5×C7×C11
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD11×D315, D11×C3⋊(C5⋊AGL(1,𝔽7)), C3×D11×D105, …
maximal normal subgroup ofD11×C3⋊(C5⋊AGL(1,𝔽7)), C3×D11×D105, AGL(1,𝔽11)×D105, …
maximal quotient ofD11×D315, C3×D11×D105, D11×C3⋊D105, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4620, 100);