Finite Group Databasebeta

← Prev (#38788013) Next (#38788015) →

C2×C3⋊((C13⋊C3)⋊AGL(1,𝔽11)) #38788014

order25740
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊((C13⋊C3)⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C3)⋊((C13⋊C3)⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C13⋊C3)⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(C3⋊(D13⋊C3))
unambiguous semidirect product(C2×C3⋊(C11⋊(D13⋊C3)))⋊C5
unambiguous semidirect product(C2×C3⋊(C13⋊AGL(1,𝔽11)))⋊C3

Splittings

Fitting, socleC2×C3×C11×C13 ⋊ C2×C3×C5
derivedC3×C11×C13 ⋊ C22×C3×C5
HallC3×C13⋊C3×C11⋊C5 ⋊ C22
HallC2×C3⋊(C11⋊(D13⋊C3)) ⋊ C5
HallC3×C11×C13⋊C3 ⋊ C22×C5
HallC13×C11⋊C5 ⋊ C2×C3×D3
HallC11×C13 ⋊ C2×C3×C5×D3
HallC3×C13⋊C3 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×C3⋊(D13⋊C3)
SylowC13 ⋊ C2×C3×C3⋊AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×C3⋊(D13⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊((C13⋊C3)⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC3×C11×C13C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C13C2×C3×C5
LCSG ▷ C3×C11×C13
UCSC1 ◁ C2

176 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 48 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) = 29
transitive degreeμt(G) = 858

A minimal faithful permutation representation — 2 generators on 29 points:

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

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 245);