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C17×C3⋊#63120 #27210577

order13260
automorphism?
homologyAbelianization (H1) = C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C3⋊#63120
unambiguous semidirect productC3⋊(C17×#63120)

Splittings

Fitting, socle, HallC3×C5×C13×C17 ⋊ C4
derived, HallC3×C5×C13 ⋊ C4×C17
HallC5×C13×C17 ⋊ Dic3
HallC3×C13×C17 ⋊ AGL(1,𝔽5)
HallC3×C5×C17 ⋊ Dic13
HallC13×C17 ⋊ ΓL(1,𝔽16)
HallC5×C17 ⋊ Dic39
HallC5×C13 ⋊ Dic3×C17
HallC3×C17 ⋊ #63120
HallC3×C13 ⋊ C17×AGL(1,𝔽5)
HallC3×C5 ⋊ C17×Dic13
SylowC13 ⋊ C17×ΓL(1,𝔽16)
SylowC5 ⋊ C17×Dic39
SylowC3 ⋊ C17×#63120

Subgroups

subgroupG/H
center, hypercenterC17C3⋊#63120
commutator, hypocenterC3×C5×C13C4×C17
FrattiniC1G
Fitting, socleC3×C5×C13×C17C4
prime radicalC3×D5×C13×C17C2
cosocleC3×D5×C13C2×C17
LCSG ▷ C3×C5×C13
UCSC1 ◁ C17

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

Conjugacy classes & character table

1377 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 127);