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C2×C17×C3⋊D165 #46778215

order33660
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C17×C3⋊D165
unambiguous semidirect product(C2×C3)⋊(C17×D165)
unambiguous semidirect product(C2×C5)⋊(C17×C3⋊D33)
unambiguous semidirect product(C2×C11)⋊(C17×C3⋊D15)

Splittings

Fitting, socleC2×C32×C5×C11×C17 ⋊ C2
derived, HallC32×C5×C11 ⋊ C22×C17
HallC32×C5×C11×C17 ⋊ C22
HallC32×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×C3⋊D3
HallC32×C5×C17 ⋊ C2×D11
HallC11×C17 ⋊ C2×C3⋊D15
HallC32×C17 ⋊ C2×D55
HallC32×C11 ⋊ C2×D5×C17
HallC5×C17 ⋊ C2×C3⋊D33
HallC5×C11 ⋊ C2×C17×C3⋊D3
HallC32×C5 ⋊ C2×C17×D11
SylowC11 ⋊ C2×C17×C3⋊D15
SylowC32 ⋊ C2×C17×D55
SylowC5 ⋊ C2×C17×C3⋊D33

Subgroups

subgroupG/H
center, hypercenterC2×C17C3⋊D165
commutator, cosocle, hypocenterC32×C5×C11C22×C17
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C17C2
LCSG ▷ C32×C5×C11
UCSC1 ◁ C2×C17

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 16830

A minimal faithful permutation representation — 3 generators on 41 points:

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

Conjugacy classes & character table

8466 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 383);