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Cayley diagram

C2×D37⋊C3 #89224

order444
isoclinismisoclinic class of D37⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×D37⋊C3
unambiguous semidirect productD37⋊(C2×C3)
unambiguous semidirect product(C37⋊C3)⋊C22
unambiguous semidirect product(C2×D37)⋊C3
unambiguous semidirect product(C2×C37⋊C3)⋊C2

Splittings

Fitting, socleC2×C37 ⋊ C2×C3
derived, SylowC37 ⋊ C22×C3
HallC2×D37 ⋊ C3
HallC37⋊C3 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2D37⋊C3
commutator, cosocle, hypocenterC37C22×C3
FrattiniC1G
Fitting, socleC2×C37C2×C3
LCSG ▷ C37
UCSC1 ◁ C2

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 74

A minimal faithful permutation representation — 2 generators on 39 points:

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

Conjugacy classes & character table

24 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×D37⋊C3, C4⋊(D37⋊C3), (C22⋊D37)⋊C3, …
maximal normal subgroup ofC4×D37⋊C3, C4⋊(D37⋊C3), (C22⋊D37)⋊C3, …
maximal quotient of(C37⋊C3)⋊Q8, C4×D37⋊C3, C4⋊(D37⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(444, 8);