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C2×C5⋊(C17⋊(D13⋊C3)) #27210515

order13260
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊(C17⋊(D13⋊C3))
unambiguous semidirect product(C2×C5)⋊(C17⋊(D13⋊C3))
unambiguous semidirect product(C2×C17)⋊(C5⋊(D13⋊C3))
unambiguous semidirect product(C2×C13⋊C3)⋊D85
unambiguous semidirect product(C2×D1105)⋊C3

Splittings

Fitting, socleC2×C5×C13×C17 ⋊ C2×C3
derived, HallC5×C13×C17 ⋊ C22×C3
HallC2×D1105 ⋊ C3
HallC5×C17×C13⋊C3 ⋊ C22
HallC17×C13⋊C3 ⋊ C2×D5
HallC13×C17 ⋊ C2×C3×D5
HallC5×C13⋊C3 ⋊ C2×D17
HallC5×C17 ⋊ C2×D13⋊C3
HallC5×C13 ⋊ C2×C3×D17
HallC13⋊C3 ⋊ C2×D85
SylowC17 ⋊ C2×C5⋊(D13⋊C3)
SylowC13 ⋊ C2×C3×D85
SylowC5 ⋊ C2×C17⋊(D13⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(C17⋊(D13⋊C3))
commutator, cosocle, hypocenterC5×C13×C17C22×C3
FrattiniC1G
Fitting, socleC2×C5×C13×C17C2×C3
LCSG ▷ C5×C13×C17
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 2210

A minimal faithful permutation representation — 2 generators on 37 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 65);