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C5×D19×D35 #27210889

order13300
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D19×D35
unambiguous semidirect product(C5×D19)⋊(C5×D7)
unambiguous semidirect product(C7×D19)⋊(C5×D5)

Splittings

Fitting, socle, HallC52×C7×C19 ⋊ C22
derivedC5×C7×C19 ⋊ C22×C5
HallC52×C19 ⋊ C2×D7
HallC52×C7 ⋊ C2×D19
HallC7×C19 ⋊ C2×C5×D5
SylowC52 ⋊ D7×D19
SylowC19 ⋊ C2×C5×D35
SylowC7 ⋊ C5×D5×D19

Subgroups

subgroupG/H
center, hypercenterC5D19×D35
commutator, cosocle, hypocenterC5×C7×C19C22×C5
FrattiniC1G
Fitting, socleC52×C7×C19C22
LCSG ▷ C5×C7×C19
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 1330

A minimal faithful permutation representation — 2 generators on 36 points:

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

Conjugacy classes & character table

1045 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13300, 47);