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C7×C13⋊C3×D35 #34062127

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

Aliases

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

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C2×C3
derivedC5×C7×C13 ⋊ C2×C3×C7
HallC5×C72×C13⋊C3 ⋊ C2
HallC7×C13×D35 ⋊ C3
HallC72×C13⋊C3 ⋊ D5
HallC72×C13 ⋊ C3×D5
HallC5×C72 ⋊ C2×C13⋊C3
HallC5×C13⋊C3 ⋊ C7×D7
HallC5×C13 ⋊ C3×C7×D7
SylowC72 ⋊ D5×C13⋊C3
SylowC13 ⋊ C3×C7×D35
SylowC5 ⋊ C7×D7×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC7C13⋊C3×D35
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

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

Relationships

maximal subgroup ofC7×D35×D13⋊C3, C7×(C5⋊(D13⋊C3))⋊D7, C7×D5×D7×C13⋊C3, …
maximal normal subgroup ofC7×D35×D13⋊C3, C7×(C5⋊(D13⋊C3))⋊D7, C7×D5×D7×C13⋊C3, …
maximal quotient ofC7×C13⋊C3×Dic35, C2×C7×C13⋊C3×D35

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 120);