Finite Group Databasebeta

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C11×C19⋊C3×A5 #49178795

order37620
automorphism?
homologyAbelianization (H1) = C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×C19⋊C3×A5
unambiguous semidirect productC19⋊(C3×C11×A5)
unambiguous semidirect product(C11×C19)⋊(C3×A5)
unambiguous semidirect product(C19×A5)⋊(C3×C11)
unambiguous semidirect product(C11×C19×A5)⋊C3

Splittings

Fitting, HallC11×C19 ⋊ C3×A5
socleC11×C19×A5 ⋊ C3
derivedC19×A5 ⋊ C3×C11
SylowC19 ⋊ C3×C11×A5

Subgroups

subgroupG/H
center, hypercenterC11C19⋊C3×A5
commutator, hypocenterC19×A5C3×C11
FrattiniC1G
FittingC11×C19C3×A5
socleC11×C19×A5C3
cosocleC19C3×C11×A5
LCSG ▷ C19×A5
UCSC1 ◁ C11

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 1045

A minimal faithful permutation representation — 2 generators on 35 points:

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

Conjugacy classes & character table

495 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 504);