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C2×C3⋊(C29⋊AGL(1,𝔽11)) #34062349

order19140
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊(C29⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C3)⋊(C29⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C29)⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊D87
unambiguous semidirect product(C2×D957)⋊C5

Splittings

Fitting, socleC2×C3×C11×C29 ⋊ C2×C5
derived, HallC3×C11×C29 ⋊ C22×C5
HallC3×C29×C11⋊C5 ⋊ C22
HallC2×D957 ⋊ C5
HallC29×C11⋊C5 ⋊ C2×D3
HallC11×C29 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×D29
HallC3×C29 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×D87
HallC3×C11 ⋊ C2×C5×D29
SylowC29 ⋊ C2×C3⋊AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D87
SylowC3 ⋊ C2×C29⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C29⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC3×C11×C29C22×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C29C2×C5
LCSG ▷ C3×C11×C29
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 1914

A minimal faithful permutation representation — 2 generators on 45 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)(31,35,36,34,39,32,33,40,37,38)(42,43);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(30,31,34,39,33,36,40,35,38,37,32)(41,42,43)(44,45)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 42);