Finite Group Databasebeta

← Prev (#46831683) Next (#46831685) →

C11×C3⋊(C3⋊(C5⋊D35)) #46831684

order34650
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C3×C5

Aliases

direct productC11×C3⋊(C3⋊(C5⋊D35))
unambiguous semidirect productC3⋊(C11×C3⋊(C5⋊D35))
unambiguous semidirect productC5⋊(C11×C3⋊D105)
unambiguous semidirect productC7⋊(C11×C3⋊(C3⋊(C5⋊D5)))

Splittings

Fitting, socle, HallC32×C52×C7×C11 ⋊ C2
derived, HallC32×C52×C7 ⋊ C2×C11
HallC32×C52×C11 ⋊ D7
HallC52×C7×C11 ⋊ C3⋊D3
HallC32×C7×C11 ⋊ C5⋊D5
HallC52×C11 ⋊ C3⋊D21
HallC32×C52 ⋊ C11×D7
HallC52×C7 ⋊ C11×C3⋊D3
HallC32×C11 ⋊ C5⋊D35
HallC7×C11 ⋊ C3⋊(C3⋊(C5⋊D5))
HallC32×C7 ⋊ C11×C5⋊D5
SylowC52 ⋊ C11×C3⋊D21
SylowC32 ⋊ C11×C5⋊D35
SylowC7 ⋊ C11×C3⋊(C3⋊(C5⋊D5))

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C3⋊(C5⋊D35))
commutator, cosocle, hypocenterC32×C52×C7C2×C11
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C32×C52×C7
UCSC1 ◁ C11

384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 17325

A minimal faithful permutation representation — 3 generators on 34 points:

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

Conjugacy classes & character table

8679 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 327);