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C5×D35⋊D19 #27210893

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

Aliases

direct productC5×D35⋊D19
unambiguous semidirect productD35⋊(C5×D19)
unambiguous semidirect productD95⋊(C5×D7)
unambiguous semidirect productD133⋊(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 ⋊ C5×D5×D7
SylowC7 ⋊ C5×D5×D19

Subgroups

subgroupG/H
center, hypercenterC5D35⋊D19
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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13300, 51);