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C2×C3⋊(C3⋊(C13⋊AGL(1,𝔽11))) #38788123

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

Aliases

direct productC2×C3⋊(C3⋊(C13⋊AGL(1,𝔽11)))
unambiguous semidirect product(C2×C3)⋊(C3⋊(C13⋊AGL(1,𝔽11)))
unambiguous semidirect product(C2×C13)⋊(C3⋊(C3⋊AGL(1,𝔽11)))
unambiguous semidirect product(C2×C11⋊C5)⋊(C3⋊D39)
unambiguous semidirect product(C2×C3⋊D429)⋊C5

Splittings

Fitting, socleC2×C32×C11×C13 ⋊ C2×C5
derived, HallC32×C11×C13 ⋊ C22×C5
HallC32×C13×C11⋊C5 ⋊ C22
HallC2×C3⋊D429 ⋊ C5
HallC13×C11⋊C5 ⋊ C2×C3⋊D3
HallC32×C11⋊C5 ⋊ C2×D13
HallC11×C13 ⋊ C2×C5×C3⋊D3
HallC32×C13 ⋊ C2×AGL(1,𝔽11)
HallC32×C11 ⋊ C2×C5×D13
HallC11⋊C5 ⋊ C2×C3⋊D39
SylowC13 ⋊ C2×C3⋊(C3⋊AGL(1,𝔽11))
SylowC11 ⋊ C2×C5×C3⋊D39
SylowC32 ⋊ C2×C13⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C3⋊(C13⋊AGL(1,𝔽11)))
commutator, cosocle, hypocenterC32×C11×C13C22×C5
FrattiniC1G
Fitting, socleC2×C32×C11×C13C2×C5
LCSG ▷ C32×C11×C13
UCSC1 ◁ C2

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 2574

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 354);