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C3×#17984456 #27210530

order13260
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#17984456

Splittings

Fitting, socle, HallC3×C5×C13×C17 ⋊ C4
derived, HallC5×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ AGL(1,𝔽5)
HallC3×C5×C17 ⋊ #261
HallC13×C17 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C13 ⋊ #595
HallC5×C17 ⋊ C3×#261
HallC5×C13 ⋊ C3×#595
HallC3×C17 ⋊ #63122
HallC3×C13 ⋊ #66775
SylowC17 ⋊ C3×#63122
HallC3×C5 ⋊ #11725130
SylowC13 ⋊ C3×#66775
SylowC5 ⋊ C3×#11725130

Subgroups

subgroupG/H
center, hypercenterC3#17984456
commutator, hypocenterC5×C13×C17C3×C4
FrattiniC1G
Fitting, socleC3×C5×C13×C17C4
prime radicalC3×D1105C2
cosocleD1105C2×C3
LCSG ▷ C5×C13×C17
UCSC1 ◁ C3

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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 80);