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Cayley diagram

D3×D37 #89227

order444
isoclinismisoclinic class of D3×D37
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD3×D37
unambiguous semidirect product(D3×C37)⋊C2
unambiguous semidirect product(C3×D37)⋊C2
unambiguous semidirect productD111⋊C2

Splittings

Fitting, socle, derived, HallC3×C37 ⋊ C22
SylowC37 ⋊ C2×D3
SylowC3 ⋊ C2×D37

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C37C22
LCSG ▷ C3×C37
UCSC1

20 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:

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#3866, C2×D3×D37, D9×D37, …
maximal normal subgroup ofD3×#3866, C2×D3×D37, D3×D37⋊C3, …
maximal quotient ofDic3×D37, D3×Dic37, #11725159, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(444, 11);