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C3×C17×#63122 #27210529

order13260
isoclinismisoclinic class of #63122
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×#63122

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C17#63122
commutator, hypocenterC5×C13C3×C4×C17
FrattiniC1G
Fitting, socleC3×C5×C13×C17C4
prime radicalC3×C17×D65C2
cosocleD65C2×C3×C17
LCSG ▷ C5×C13
UCSC1 ◁ C3×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:

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

Conjugacy classes & character table

1020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 79);