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C2×C5×C11⋊(D49⋊C3) #44568369

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C11⋊(D49⋊C3)
unambiguous semidirect product(C2×C49⋊C3)⋊(C5×D11)
unambiguous semidirect product(C2×C5×D539)⋊C3

Splittings

FittingC2×C5×C11×C49 ⋊ C2×C3
derived, HallC11×C49 ⋊ C22×C3×C5
HallC2×C5×D539 ⋊ C3
HallC5×C11×C49⋊C3 ⋊ C22
HallC5×C11×C49 ⋊ C22×C3
HallC2×D539 ⋊ C3×C5
HallC11×C49⋊C3 ⋊ C22×C5
HallC5×C49⋊C3 ⋊ C2×D11
HallC5×C49 ⋊ C2×C3×D11
HallC49⋊C3 ⋊ C2×C5×D11
HallC5×C11 ⋊ C2×D49⋊C3
SylowC49 ⋊ C2×C3×C5×D11
SylowC11 ⋊ C2×C5×D49⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5C11⋊(D49⋊C3)
commutator, cosocle, hypocenterC11×C49C22×C3×C5
FrattiniC7C2×C5×C11⋊AGL(1,𝔽7)
FittingC2×C5×C11×C49C2×C3
socleC2×C5×C7×C11AGL(1,𝔽7)
LCSG ▷ C11×C49
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 67
transitive degreeμt(G) = 5390

A minimal faithful permutation representation — 2 generators on 67 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(13,21,23,15,16,24)(14,33,35,19,20,36)(17,45,32,26,27,54)(18,50,51,30,31,60)(22,29,28,34,39,47)(25,48,57,43,44,58)(37,49,52,55,38,41)(40,53,42,56,46,59)(61,62,63,64,65);(1,2,4,6,8,10,11,9,7,5,3)(12,34,31,42,41,46,15,19,56,25,24,51,26,30,33,57,16,45,47,39,54,35,55,49,48,44,38,37,36,32,29,28,27,21,58,20,18,17,60,23,43,40,14,13,53,52,59,50,22)(66,67)

Conjugacy classes & character table

1090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 71);