Finite Group Databasebeta

← Prev (#27210572) Next (#27210574) →

C17×C3⋊#63121 #27210573

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

Aliases

direct productC17×C3⋊#63121
unambiguous semidirect productC3⋊(C17×#63121)

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 ⋊ #261
HallC13×C17 ⋊ ΓL(1,𝔽16)
HallC5×C17 ⋊ C3⋊#261
HallC5×C13 ⋊ Dic3×C17
HallC3×C17 ⋊ #63121
HallC3×C13 ⋊ C17×AGL(1,𝔽5)
HallC3×C5 ⋊ C17×#261
SylowC13 ⋊ C17×ΓL(1,𝔽16)
SylowC5 ⋊ C17×C3⋊#261
SylowC3 ⋊ C17×#63121

Subgroups

subgroupG/H
center, hypercenterC17C3⋊#63121
commutator, hypocenterC3×C5×C13C4×C17
FrattiniC1G
Fitting, socleC3×C5×C13×C17C4
prime radicalC3×C17×D65C2
cosocleC3×D65C2×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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 123);