Finite Group Databasebeta

← Prev (#30633585) Next (#30633587) →

C3×C7×C11×D35 #30633586

order16170
isoclinismisoclinic class of D35
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C11×D35
unambiguous semidirect productC5⋊(C3×C7×C11×D7)

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C2
derivedC5×C7 ⋊ C2×C3×C7×C11
HallC5×C72×C11 ⋊ C2×C3
HallC3×C72×C11 ⋊ D5
HallC3×C5×C72 ⋊ C2×C11
HallC72×C11 ⋊ C3×D5
HallC5×C72 ⋊ C2×C3×C11
HallC3×C5×C11 ⋊ C7×D7
HallC3×C72 ⋊ D5×C11
HallC5×C11 ⋊ C3×C7×D7
SylowC72 ⋊ C3×D5×C11
HallC3×C5 ⋊ C7×C11×D7
SylowC5 ⋊ C3×C7×C11×D7

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11D35
commutator, cosocle, hypocenterC5×C7C2×C3×C7×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C2
LCSG ▷ C5×C7
UCSC1 ◁ C3×C7×C11

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

4389 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C7×D11×D35, C3×C7×D5×C11×D7, C3×C7×D35⋊D11, …
maximal normal subgroup ofC3×C7×D11×D35, C3×C7×D5×C11×D7, C3×C7×D35⋊D11, …
maximal quotient ofC3×C7×C11×Dic35, C2×C3×C7×C11×D35

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 131);