Finite Group Databasebeta

← Prev (#46778009) Next (#46778011) →

D51×C3⋊AGL(1,𝔽11) #46778010

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

Aliases

direct productD51×C3⋊AGL(1,𝔽11)
unambiguous semidirect product(D33×D51)⋊C5

Splittings

Fitting, socle, derived, HallC32×C11×C17 ⋊ C22×C5
HallC32×C17×C11⋊C5 ⋊ C22
HallD33×D51 ⋊ C5
HallC17×C11⋊C5 ⋊ D32
HallC32×C11⋊C5 ⋊ C2×D17
HallC11×C17 ⋊ C5×D32
HallC32×C17 ⋊ C2×AGL(1,𝔽11)
HallC32×C11 ⋊ C2×C5×D17
HallC11⋊C5 ⋊ D3×D51
SylowC17 ⋊ D3×C3⋊AGL(1,𝔽11)
SylowC11 ⋊ C5×D3×D51
SylowC32 ⋊ D17×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C11×C17C22×C5
LCSG ▷ C32×C11×C17
UCSC1

176 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 1122

A minimal faithful permutation representation — 2 generators on 34 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 178);