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C4×C13⋊C3×C43⋊C3 #34117478

order20124
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC4×C13⋊C3×C43⋊C3
unambiguous semidirect product(C4×C13×C43⋊C3)⋊C3
unambiguous semidirect product(C4×C13⋊C3×C43)⋊C3
unambiguous semidirect product(C4×#13131976)⋊C3
unambiguous semidirect product(C4×#13131975)⋊C3

Splittings

Fitting, HallC4×C13×C43 ⋊ C32
derived, HallC13×C43 ⋊ C32×C4
HallC4×C43 ⋊ C3×C13⋊C3
HallC4×C13 ⋊ C3×C43⋊C3
SylowC43 ⋊ C3×C4×C13⋊C3
SylowC13 ⋊ C3×C4×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC4C13⋊C3×C43⋊C3
commutator, hypocenterC13×C43C32×C4
FrattiniC2C2×C13⋊C3×C43⋊C3
FittingC4×C13×C43C32
socle, cosocleC2×C13×C43C2×C32
prime radicalC2×C13⋊C3×C43⋊C3C2
LCSG ▷ C13×C43
UCSC1 ◁ C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 60
transitive degreeμt(G) = 2236

A minimal faithful permutation representation — 2 generators on 60 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,33)(18,26,31)(21,29,28)(23,32,25)(27,36,40)(30,37,39)(34,41,35)(38,42,43)(44,45,47,46,49,53,50,54,56,48,51,55,52)(57,58,59,60);(1,2,4,8,15,20,5,9,16,25,35,32,12,19,28,24,34,41,22,31,39,36,14,23,33,40,43,42,26,7,13,21,30,38,37,17,3,6,11,18,27,29,10)(45,46,48)(47,50,53)(49,52,51)(54,56,55)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20124, 81);