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C17×Dic65⋊C3 #27210473

order13260
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×Dic65⋊C3
unambiguous semidirect productDic65⋊(C3×C17)
unambiguous semidirect product(C17×Dic65)⋊C3

Splittings

derived, HallC5×C13 ⋊ C3×C4×C17
HallC17×Dic65 ⋊ C3
HallC5×C17×C13⋊C3 ⋊ C4
HallC5×C13×C17 ⋊ C3×C4
HallC17×C13⋊C3 ⋊ Dic5
HallDic65 ⋊ C3×C17
HallC13×C17 ⋊ C3×Dic5
HallC5×C13⋊C3 ⋊ C4×C17
HallC5×C17 ⋊ Dic13⋊C3
HallC13⋊C3 ⋊ C17×Dic5
SylowC13 ⋊ C3×C17×Dic5
SylowC5 ⋊ C17×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C17C5⋊(D13⋊C3)
commutator, hypocenterC5×C13C3×C4×C17
FrattiniC2C17×C5⋊(D13⋊C3)
Fitting, socleC2×C5×C13×C17C2×C3
prime radicalC2×C5×C17×C13⋊C3C2
cosocleC2×C5×C13C2×C3×C17
LCSG ▷ C5×C13
UCSC1 ◁ C2×C17

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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 23);