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C7×C13⋊C3×A5 #30655804

order16380
automorphism?
homologyAbelianization (H1) = C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×C13⋊C3×A5
unambiguous semidirect productC13⋊(C3×C7×A5)
unambiguous semidirect product(C13×A5)⋊(C3×C7)

Splittings

Fitting, HallC7×C13 ⋊ C3×A5
socleC7×C13×A5 ⋊ C3
derivedC13×A5 ⋊ C3×C7
SylowC13 ⋊ C3×C7×A5

Subgroups

subgroupG/H
center, hypercenterC7C13⋊C3×A5
commutator, hypocenterC13×A5C3×C7
FrattiniC1G
FittingC7×C13C3×A5
socleC7×C13×A5C3
cosocleC13C3×C7×A5
LCSG ▷ C13×A5
UCSC1 ◁ C7

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 25
transitive degreeμt(G) = 455

A minimal faithful permutation representation — 2 generators on 25 points:

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

Conjugacy classes & character table

245 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 854);