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C3×D4×C11⋊C5 #13050335

order1320
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×D4×C11⋊C5
unambiguous semidirect productC4⋊(C2×C3×C11⋊C5)
unambiguous semidirect product(D4×C11)⋊(C3×C5)
unambiguous semidirect product(C3×D4×C11)⋊C5

Splittings

Fitting, HallC3×D4×C11 ⋊ C5
HallD4×C11 ⋊ C3×C5
HallC3×C11 ⋊ C5×D4
SylowC11 ⋊ C3×C5×D4

Subgroups

subgroupG/H
centerC2×C3C22×C11⋊C5
commutator, cosocleC2×C11C22×C3×C5
FrattiniC2C22×C3×C11⋊C5
FittingC3×D4×C11C5
socleC2×C3×C11C22×C5
hypercenterC3×D4C11⋊C5
hypocenterC11C3×C5×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C3 ◁ C3×D4

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 132

A minimal faithful permutation representation — 2 generators on 18 points:

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

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D4×AGL(1,𝔽11), D3×D4×C11⋊C5, D4×C3⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×D4×AGL(1,𝔽11), D3×D4×C11⋊C5, D4×C3⋊AGL(1,𝔽11), …
maximal quotient ofC2×C3×D4×C11⋊C5, C3×D8×C11⋊C5, C3×SD16×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 39);