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C7×C5⋊((C13⋊C3)⋊D7) #34062126

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C5⋊((C13⋊C3)⋊D7)
unambiguous semidirect productC5⋊(C7×(C13⋊C3)⋊D7)
unambiguous semidirect product(C13⋊C3)⋊(C7×D35)

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C2×C3
derivedC5×C7×C13 ⋊ C2×C3×C7
HallC5×C72×C13⋊C3 ⋊ C2
HallC7×D455 ⋊ C3
HallC72×C13⋊C3 ⋊ D5
HallC72×C13 ⋊ C3×D5
HallC5×C72 ⋊ D13⋊C3
HallC5×C13⋊C3 ⋊ C7×D7
HallC5×C13 ⋊ C3×C7×D7
SylowC72 ⋊ C5⋊(D13⋊C3)
HallC13⋊C3 ⋊ C7×D35
SylowC13 ⋊ C3×C7×D35
SylowC5 ⋊ C7×(C13⋊C3)⋊D7

Subgroups

subgroupG/H
center, hypercenterC7C5⋊((C13⋊C3)⋊D7)
commutator, cosocle, hypocenterC5×C7×C13C2×C3×C7
FrattiniC1G
Fitting, socleC5×C72×C13C2×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C7

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 910

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×D35×D13⋊C3, C7×D7×C5⋊(D13⋊C3), C7×D5×(C13⋊C3)⋊D7, …
maximal normal subgroup ofC7×D35×D13⋊C3, C7×D7×C5⋊(D13⋊C3), C7×D5×(C13⋊C3)⋊D7, …
maximal quotient ofC7×#19129703, C2×C7×C5⋊((C13⋊C3)⋊D7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 119);