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C5×Dic221⋊C3 #27210470

order13260
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic221⋊C3
unambiguous semidirect productDic221⋊(C3×C5)
unambiguous semidirect product(C5×Dic221)⋊C3

Splittings

derived, HallC13×C17 ⋊ C3×C4×C5
HallC5×Dic221 ⋊ C3
HallC5×C17×C13⋊C3 ⋊ C4
HallC5×C13×C17 ⋊ C3×C4
HallDic221 ⋊ C3×C5
HallC17×C13⋊C3 ⋊ C4×C5
HallC5×C13⋊C3 ⋊ Dic17
HallC5×C17 ⋊ Dic13⋊C3
HallC5×C13 ⋊ C3×Dic17
HallC13⋊C3 ⋊ C5×Dic17
SylowC17 ⋊ C5×Dic13⋊C3
SylowC13 ⋊ C3×C5×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C5C17⋊(D13⋊C3)
commutator, hypocenterC13×C17C3×C4×C5
FrattiniC2C5×C17⋊(D13⋊C3)
Fitting, socleC2×C5×C13×C17C2×C3
prime radicalC2×C5×C17×C13⋊C3C2
cosocleC2×C13×C17C2×C3×C5
LCSG ▷ C13×C17
UCSC1 ◁ C2×C5

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 20);