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C2×C5×D1683 #46777942

order33660
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D1683
unambiguous semidirect product(C2×C9)⋊(C5×D187)
unambiguous semidirect product(C2×C17)⋊(C5×D99)

Splittings

FittingC2×C5×C9×C11×C17 ⋊ C2
derived, HallC9×C11×C17 ⋊ C22×C5
HallC5×C9×C11×C17 ⋊ C22
HallC5×C11×C17 ⋊ C2×D9
HallC5×C9×C17 ⋊ C2×D11
HallC5×C9×C11 ⋊ C2×D17
HallC11×C17 ⋊ C2×C5×D9
HallC9×C17 ⋊ C2×C5×D11
HallC9×C11 ⋊ C2×C5×D17
HallC5×C17 ⋊ C2×D99
HallC5×C11 ⋊ C2×D153
HallC5×C9 ⋊ C2×D187
SylowC17 ⋊ C2×C5×D99
SylowC11 ⋊ C2×C5×D153
SylowC9 ⋊ C2×C5×D187

Subgroups

subgroupG/H
center, hypercenterC2×C5D1683
commutator, cosocle, hypocenterC9×C11×C17C22×C5
FrattiniC3C2×C5×D561
FittingC2×C5×C9×C11×C17C2
socleC2×C3×C5×C11×C17D3
LCSG ▷ C9×C11×C17
UCSC1 ◁ C2×C5

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:

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

Conjugacy classes & character table

8430 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 110);