Finite Group Databasebeta

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C3×C13×#66774 #27210528

order13260
isoclinismisoclinic class of #66774
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×#66774

Splittings

Fitting, socle, HallC3×C5×C13×C17 ⋊ C4
derived, HallC5×C17 ⋊ C3×C4×C13
HallC5×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ AGL(1,𝔽5)
HallC3×C5×C17 ⋊ C4×C13
HallC13×C17 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C13 ⋊ Dic17
HallC5×C13 ⋊ C3×Dic17
HallC3×C17 ⋊ C13×AGL(1,𝔽5)
SylowC17 ⋊ C3×C13×AGL(1,𝔽5)
HallC3×C5 ⋊ C13×Dic17
SylowC5 ⋊ C3×C13×Dic17

Subgroups

subgroupG/H
center, hypercenterC3×C13#66774
commutator, hypocenterC5×C17C3×C4×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C17C4
prime radicalC3×D5×C13×C17C2
cosocleD5×C17C2×C3×C13
LCSG ▷ C5×C17
UCSC1 ◁ C3×C13

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

Conjugacy classes & character table

1443 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 78);