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C13×C5⋊#64418 #34062174

order19110
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C5⋊#64418
unambiguous semidirect productC5⋊(C13×#64418)

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ D3
derived, HallC5×#3862 ⋊ C2×C13
HallC5×C13×#3862 ⋊ C2
HallC13×#3862 ⋊ D5
HallC72×C13 ⋊ D15
HallC5×C72 ⋊ D3×C13
Hall#3862 ⋊ D5×C13
HallC5×C13 ⋊ #64418
SylowC72 ⋊ C13×D15
SylowC5 ⋊ C13×#64418

Subgroups

subgroupG/H
center, hypercenterC13C5⋊#64418
commutator, cosocle, hypocenterC5×#3862C2×C13
FrattiniC1G
Fitting, socleC5×C72×C13D3
LCSG ▷ C5×#3862
UCSC1 ◁ C13

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 910

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD13×C5⋊#64418, D5×C13×#64418, D65⋊#64418, …
maximal normal subgroup ofD13×C5⋊#64418, D5×C13×#64418, D65⋊#64418, …
maximal quotient ofC13×#15668724, C2×C13×C5⋊#64418

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 167);