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C13×C3⋊((C43⋊C3)⋊C4) #34117491

order20124
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊((C43⋊C3)⋊C4)
unambiguous semidirect productC3⋊(C13×(C43⋊C3)⋊C4)
unambiguous semidirect product(C43⋊C3)⋊(Dic3×C13)
unambiguous semidirect productDic129⋊(C3×C13)

Splittings

derivedC3×C43 ⋊ C3×C4×C13
HallC3×C13×C43⋊C3 ⋊ C4
HallC13×C43 ⋊ C3×Dic3
HallC3×C43⋊C3 ⋊ C4×C13
SylowC43 ⋊ C3×Dic3×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13C3⋊(D43⋊C3)
commutator, hypocenterC3×C43C3×C4×C13
FrattiniC2C13×C3⋊(D43⋊C3)
Fitting, socleC2×C3×C13×C43C2×C3
prime radicalC2×C3×C13×C43⋊C3C2
cosocleC2×C3×C43C2×C3×C13
LCSG ▷ C3×C43
UCSC1 ◁ C2×C13

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 63
transitive degreeμt(G) = 6708

A minimal faithful permutation representation — 2 generators on 63 points:

(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,37)(12,26,22,20,16,13)(19,29,34,21,30,40)(23,25,39,31,32,35)(33,38,42,36,41,43)(45,46)(47,48,49,50)(51,52,53,54,55,56,57,58,59,60,61,62,63);(1,2,5,11,19,20,4,8,13,23,33,32,10,16,24,34,42,41,18,29,35,37,28,39,30,27,38,43,40,15,26,14,25,36,31,22,7,6,12,21,17,9,3)(44,45,46)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20124, 94);