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C13×C3⋊#66774 #27210568

order13260
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊#66774
unambiguous semidirect productC3⋊(C13×#66774)

Splittings

Fitting, socle, HallC3×C5×C13×C17 ⋊ C4
derived, HallC3×C5×C17 ⋊ C4×C13
HallC5×C13×C17 ⋊ Dic3
HallC3×C13×C17 ⋊ AGL(1,𝔽5)
HallC13×C17 ⋊ ΓL(1,𝔽16)
HallC3×C5×C13 ⋊ Dic17
HallC5×C17 ⋊ Dic3×C13
HallC5×C13 ⋊ Dic51
HallC3×C17 ⋊ C13×AGL(1,𝔽5)
HallC3×C13 ⋊ #66774
SylowC17 ⋊ C13×ΓL(1,𝔽16)
HallC3×C5 ⋊ C13×Dic17
SylowC5 ⋊ C13×Dic51
SylowC3 ⋊ C13×#66774

Subgroups

subgroupG/H
center, hypercenterC13C3⋊#66774
commutator, hypocenterC3×C5×C17C4×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C17C4
prime radicalC3×D5×C13×C17C2
cosocleC3×D5×C17C2×C13
LCSG ▷ C3×C5×C17
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 3315

A minimal faithful permutation representation — 2 generators on 38 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(19,20,21,22)(24,25)(26,27,28,29,30,31,32,33,34,35,36,37,38);(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)(18,19,20,22,21)(23,24,25)

Conjugacy classes & character table

1365 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 118);