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C13×C5⋊#64425 #34062134

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C7

Aliases

direct productC13×C5⋊#64425
unambiguous semidirect productC5⋊(C13×#64425)

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C2×C3
derived, HallC5×C72 ⋊ C2×C3×C13
HallC5×C13×#3862 ⋊ C2
HallC13×C5⋊(C7⋊D7) ⋊ C3
HallC13×#3862 ⋊ D5
HallC5×#3862 ⋊ C2×C13
HallC72×C13 ⋊ C3×D5
HallC5⋊(C7⋊D7) ⋊ C3×C13
Hall#3862 ⋊ D5×C13
HallC5×C13 ⋊ #64425
SylowC72 ⋊ C3×D5×C13
SylowC5 ⋊ C13×#64425

Subgroups

subgroupG/H
center, hypercenterC13C5⋊#64425
commutator, cosocle, hypocenterC5×C72C2×C3×C13
FrattiniC1G
Fitting, socleC5×C72×C13C2×C3
LCSG ▷ C5×C72
UCSC1 ◁ C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1365

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC13×#15668774, #50303819, C13×#64418⋊D5, …
maximal normal subgroup ofC13×#15668774, #50303819, C13×#64418⋊D5, …
maximal quotient ofC13×#15668735, C2×C13×C5⋊#64425

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 127);