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C2×C11×C3⋊D255 #46778214

order33660
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C11×C3⋊D255
unambiguous semidirect product(C2×C3)⋊(C11×D255)
unambiguous semidirect product(C2×C5)⋊(C11×C3⋊D51)
unambiguous semidirect product(C2×C17)⋊(C11×C3⋊D15)

Splittings

Fitting, socleC2×C32×C5×C11×C17 ⋊ C2
derived, HallC32×C5×C17 ⋊ C22×C11
HallC32×C5×C11×C17 ⋊ C22
HallC32×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×C3⋊D3
HallC32×C5×C11 ⋊ C2×D17
HallC11×C17 ⋊ C2×C3⋊D15
HallC32×C17 ⋊ C2×D5×C11
HallC32×C11 ⋊ C2×D85
HallC5×C17 ⋊ C2×C11×C3⋊D3
HallC5×C11 ⋊ C2×C3⋊D51
HallC32×C5 ⋊ C2×C11×D17
SylowC17 ⋊ C2×C11×C3⋊D15
SylowC32 ⋊ C2×C11×D85
SylowC5 ⋊ C2×C11×C3⋊D51

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊D255
commutator, cosocle, hypocenterC32×C5×C17C22×C11
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C17C2
LCSG ▷ C32×C5×C17
UCSC1 ◁ C2×C11

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)(14,15,16,17,18,19,20,21,22,23,24)(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)(25,26,28,30,32,34,36,38,40,41,39,37,35,33,31,29,27);(3,4,5)

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, 382);