Finite Group Databasebeta

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C5×C72×D13⋊C3 #34062057

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC5×C72×D13⋊C3
unambiguous semidirect productD13⋊(C3×C5×C72)
unambiguous semidirect product(C13⋊C3)⋊(C2×C5×C72)
unambiguous semidirect product(C5×D13)⋊(C3×C72)

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C5×C72
HallC5×C72×C13⋊C3 ⋊ C2
HallC5×C72×D13 ⋊ C3
HallC72×C13⋊C3 ⋊ C2×C5
HallC72×D13 ⋊ C3×C5
HallC72×C13 ⋊ C2×C3×C5
HallC5×C13⋊C3 ⋊ C2×C72
HallC5×D13 ⋊ C3×C72
HallC5×C13 ⋊ C2×C3×C72
HallC13⋊C3 ⋊ C2×C5×C72
HallD13 ⋊ C3×C5×C72

Subgroups

subgroupG/H
center, hypercenterC5×C72D13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C5×C72
FrattiniC1G
Fitting, socleC5×C72×C13C2×C3
LCSG ▷ C13
UCSC1 ◁ C5×C72

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3185

Conjugacy classes & character table

1960 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C72×AGL(1,𝔽13), C5×C7×#11763979, C5×C7×D7×D13⋊C3, …
maximal normal subgroup ofC5×C72×AGL(1,𝔽13), C5×C7×#11763979, C5×C7×D7×D13⋊C3, …
maximal quotient ofC5×C72×Dic13⋊C3, C2×C5×C72×D13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 50);