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D12×C11⋊C5 #13050326

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

Aliases

direct productD12×C11⋊C5
unambiguous semidirect productC4⋊(D3×C11⋊C5)
unambiguous semidirect product(C11×D12)⋊C5

Splittings

FittingC3×C4×C11 ⋊ C2×C5
HallC11×D12 ⋊ C5
HallC3×C11⋊C5 ⋊ D4
HallC3×C11 ⋊ C5×D4
SylowC11 ⋊ C5×D12
SylowC3 ⋊ D4×C11⋊C5

Subgroups

subgroupG/H
center, FrattiniC2C2×D3×C11⋊C5
commutator, socle, cosocleC2×C3×C11C22×C5
FittingC3×C4×C11C2×C5
hypercenterC4D3×C11⋊C5
hypocenterC3×C11C5×D4
LCSG ▷ C2×C3×C11 ▷ C3×C11
UCSC1 ◁ C2 ◁ C4

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

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D4×C11⋊C5, #72216746, D12×AGL(1,𝔽11), …
maximal normal subgroup ofD3×D4×C11⋊C5, #72216746, D12×AGL(1,𝔽11), …
maximal quotient ofC2×D12×C11⋊C5, D24×C11⋊C5, #204×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 30);