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D3×#3866⋊C3 #72228575

order2664
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productD3×#3866⋊C3

Splittings

Fitting, socle, derivedC3×C37 ⋊ C2×C3×C4
HallC3×C37⋊C3 ⋊ C2×C4
SylowC37 ⋊ C3×C4×D3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C37C2×C3×C4
prime radicalD3×D37⋊C3C2
cosocleC3×D37C22×C3
LCSG ▷ C3×C37
UCSC1

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 111

A minimal faithful permutation representation — 2 generators on 40 points:

(2,7,12,8,4,17,5,18,10,3,11,25)(6,27,37,24,14,26,15,30,28,13,29,34)(9,16,36,20,21,32,22,33,35,19,31,23)(38,39,40);(1,2,6,16,32,22,8,20,18,34,10,11,24,36,17,14,30,37,21,31,28,27,29,25,35,13,4,12,26,7,19,3,9,23,33,15,5)(39,40)

Conjugacy classes & character table

45 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽37), S4×#3866⋊C3, C2×D3×#3866⋊C3, …
maximal normal subgroup ofD3×AGL(1,𝔽37), C2×D3×#3866⋊C3
maximal quotient ofS4×#3866⋊C3, C2×D3×#3866⋊C3, C3⋊D3×#3866⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((2,7,12,8,4,17,5,18,10,3,11,25)(6,27,37,24,14,26,15,30,28,13,29,34)(9,16,36,20,21,32,22,33,35,19,31,23)(38,39,40), (1,2,6,16,32,22,8,20,18,34,10,11,24,36,17,14,30,37,21,31,28,27,29,25,35,13,4,12,26,7,19,3,9,23,33,15,5)(39,40));