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D3×C7×C11⋊C5 #14556339

order2310
isoclinismisoclinic class of D3×C11⋊C5
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC7D3×C11⋊C5
commutator, cosocle, hypocenterC3×C11C2×C5×C7
FrattiniC1G
Fitting, socleC3×C7×C11C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 231

A minimal faithful permutation representation — 2 generators on 21 points:

(1,2,3)(4,5,6,7,8,9,10)(12,13,15,18,17)(14,16,20,21,19);(2,3)(11,12,14,17,13,15,19,21,16,18,20)

Conjugacy classes & character table

147 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C7×AGL(1,𝔽11), D3×C7⋊AGL(1,𝔽11), D3×D7×C11⋊C5, …
maximal normal subgroup ofD3×C7×AGL(1,𝔽11), D3×C7⋊AGL(1,𝔽11), D3×D7×C11⋊C5, …
maximal quotient ofC7×Dic3×C11⋊C5, C2×D3×C7×C11⋊C5, D3×C7×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2310, 23);