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C3⋊#17984466 #27210580

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

Aliases

unambiguous semidirect productC3⋊#17984466

Splittings

Fitting, socle, derived, HallC3×C5×C13×C17 ⋊ C4
HallC5×C13×C17 ⋊ Dic3
HallC3×C13×C17 ⋊ AGL(1,𝔽5)
HallC3×C5×C17 ⋊ Dic13
HallC13×C17 ⋊ ΓL(1,𝔽16)
HallC3×C5×C13 ⋊ Dic17
HallC5×C17 ⋊ Dic39
HallC5×C13 ⋊ Dic51
HallC3×C17 ⋊ #63120
HallC3×C13 ⋊ #66774
SylowC17 ⋊ C3⋊#63120
HallC3×C5 ⋊ Dic221
SylowC13 ⋊ C3⋊#66774
SylowC5 ⋊ Dic663
SylowC3 ⋊ #17984466

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C13×C17C4
prime radical, cosocleC3×D5×C13×C17C2
LCSG ▷ C3×C5×C13×C17
UCSC1

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

Polycyclic presentation:

2^2,3,5,13,17|a^2=b,c^a=c^2,d^a=d^2,e^a=e^12,f^a=f^16,d^b=d^4

Conjugacy classes & character table

1329 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 130);