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D35×#63270 #34062169

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

Aliases

direct productD35×#63270
unambiguous semidirect productC5⋊(D7×#63270)

Splittings

Fitting, socle, derived, HallC5×C72×C13 ⋊ C2×C3
HallC5×C7×#63270 ⋊ C2
HallC7×C13×D35 ⋊ C3
HallC7×#63270 ⋊ D5
HallC72×C13 ⋊ C3×D5
HallC7×D35 ⋊ C13⋊C3
HallC5×C72 ⋊ C2×C13⋊C3
HallC5×C13 ⋊ D7×ΓL(1,𝔽8)
SylowC72 ⋊ D5×C13⋊C3
SylowC13 ⋊ ΓL(1,𝔽8)×D35
SylowC5 ⋊ D7×#63270

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C13C2×C3
LCSG ▷ C5×C72×C13
UCSC1

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD35×#10587722, D35×#10587720, #50304055, …
maximal normal subgroup ofD35×#10587722, D35×#10587720, #50304055, …
maximal quotient ofDic35×#63270, C2×D35×#63270

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 162);