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C2×C11×D819 #49114508

order36036
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D819
unambiguous semidirect product(C2×C7)⋊(C11×D117)
unambiguous semidirect product(C2×C9)⋊(C11×D91)
unambiguous semidirect product(C2×C13)⋊(C11×D63)

Splittings

FittingC2×C7×C9×C11×C13 ⋊ C2
derived, HallC7×C9×C13 ⋊ C22×C11
HallC7×C9×C11×C13 ⋊ C22
HallC9×C11×C13 ⋊ C2×D7
HallC7×C11×C13 ⋊ C2×D9
HallC7×C9×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×D63
HallC9×C13 ⋊ C2×C11×D7
HallC9×C11 ⋊ C2×D91
HallC7×C13 ⋊ C2×C11×D9
HallC7×C11 ⋊ C2×D117
HallC7×C9 ⋊ C2×C11×D13
SylowC13 ⋊ C2×C11×D63
SylowC9 ⋊ C2×C11×D91
SylowC7 ⋊ C2×C11×D117

Subgroups

subgroupG/H
center, hypercenterC2×C11D819
commutator, cosocle, hypocenterC7×C9×C13C22×C11
FrattiniC3C2×C11×D273
FittingC2×C7×C9×C11×C13C2
socleC2×C3×C7×C11×C13D3
LCSG ▷ C7×C9×C13
UCSC1 ◁ C2×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 18018

A minimal faithful permutation representation — 2 generators on 42 points:

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

Conjugacy classes & character table

9042 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 176);