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Cayley diagram

D3×D41 #92451

order492
isoclinismisoclinic class of D3×D41
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD3×D41
unambiguous semidirect product(D3×C41)⋊C2
unambiguous semidirect product(C3×D41)⋊C2
unambiguous semidirect productD123⋊C2

Splittings

Fitting, socle, derived, HallC3×C41 ⋊ C22
SylowC41 ⋊ C2×D3
SylowC3 ⋊ C2×D41

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C41C22
LCSG ▷ C3×C41
UCSC1

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 123

A minimal faithful permutation representation — 2 generators on 44 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)(40,41)(42,43,44);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(43,44)

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#4223, C2×D3×D41, D9×D41, …
maximal normal subgroup ofD3×#4223, C2×D3×D41, C3×D3×D41, …
maximal quotient ofDic3×D41, D3×Dic41, #11758295, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(492, 7);