Finite Group Databasebeta

← Prev (#34062169) Next (#34062171) →

D35×#63271 #34062170

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

Aliases

direct productD35×#63271
unambiguous semidirect productC5⋊(D7×#63271)

Splittings

Fitting, socle, derived, HallC5×C72×C13 ⋊ C2×C3
HallC5×C7×#63271 ⋊ C2
HallC7×C13×D35 ⋊ C3
HallC7×#63271 ⋊ 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×#63271

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×#10587723, D35×#10587721, #50304056, …
maximal normal subgroup ofD35×#10587723, D35×#10587721, #50304056, …
maximal quotient ofDic35×#63271, C2×D35×#63271

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 163);