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C13⋊C3×Dic85 #27210472

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

Aliases

direct productC13⋊C3×Dic85
unambiguous semidirect product(C13×Dic85)⋊C3

Splittings

derived, HallC5×C13×C17 ⋊ C3×C4
HallC13×Dic85 ⋊ C3
HallC5×C17×C13⋊C3 ⋊ C4
HallC17×C13⋊C3 ⋊ Dic5
HallC13×C17 ⋊ C3×Dic5
HallC5×C13⋊C3 ⋊ Dic17
HallC5×C17 ⋊ C4×C13⋊C3
HallC5×C13 ⋊ C3×Dic17
SylowC17 ⋊ Dic5×C13⋊C3
SylowC13 ⋊ C3×Dic85
SylowC5 ⋊ C13⋊C3×Dic17

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C13⋊C3×D85
commutator, hypocenterC5×C13×C17C3×C4
Fitting, socle, cosocleC2×C5×C13×C17C2×C3
prime radicalC2×C5×C17×C13⋊C3C2
LCSG ▷ C5×C13×C17
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 4420

A minimal faithful permutation representation — 2 generators on 39 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(19,20)(21,22)(24,25,27)(26,29,32)(28,31,30)(33,35,34)(36,39,38,37);(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)(18,19,21,22,20)(23,24,26,25,28,32,29,33,35,27,30,34,31)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 22);