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C2×C11×D765 #46777940

order33660
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D765
unambiguous semidirect product(C2×C5)⋊(C11×D153)
unambiguous semidirect product(C2×C9)⋊(C11×D85)
unambiguous semidirect product(C2×C17)⋊(C11×D45)

Splittings

FittingC2×C5×C9×C11×C17 ⋊ C2
derived, HallC5×C9×C17 ⋊ C22×C11
HallC5×C9×C11×C17 ⋊ C22
HallC9×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×D9
HallC5×C9×C11 ⋊ C2×D17
HallC11×C17 ⋊ C2×D45
HallC9×C17 ⋊ C2×D5×C11
HallC9×C11 ⋊ C2×D85
HallC5×C17 ⋊ C2×C11×D9
HallC5×C11 ⋊ C2×D153
HallC5×C9 ⋊ C2×C11×D17
SylowC17 ⋊ C2×C11×D45
SylowC9 ⋊ C2×C11×D85
SylowC5 ⋊ C2×C11×D153

Subgroups

subgroupG/H
center, hypercenterC2×C11D765
commutator, cosocle, hypocenterC5×C9×C17C22×C11
FrattiniC3C2×C11×D255
FittingC2×C5×C9×C11×C17C2
socleC2×C3×C5×C11×C17D3
LCSG ▷ C5×C9×C17
UCSC1 ◁ C2×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 16830

A minimal faithful permutation representation — 2 generators on 44 points:

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

Conjugacy classes & character table

8448 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 108);