Finite Group Databasebeta

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C3×C11⋊C5×C7⋊D7 #30633519

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C7

Aliases

direct productC3×C11⋊C5×C7⋊D7
unambiguous semidirect product(C3×C11×C7⋊D7)⋊C5

Splittings

Fitting, socle, HallC3×C72×C11 ⋊ C2×C5
derived, HallC72×C11 ⋊ C2×C3×C5
HallC3×C72×C11⋊C5 ⋊ C2
HallC3×C11×C7⋊D7 ⋊ C5
HallC72×C11⋊C5 ⋊ C2×C3
HallC11×C7⋊D7 ⋊ C3×C5
HallC3×C72 ⋊ C2×C11⋊C5
SylowC72 ⋊ C2×C3×C11⋊C5
HallC3×C11 ⋊ C5×C7⋊D7
SylowC11 ⋊ C3×C5×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC3C11⋊C5×C7⋊D7
commutator, cosocle, hypocenterC72×C11C2×C3×C5
FrattiniC1G
Fitting, socleC3×C72×C11C2×C5
LCSG ▷ C72×C11
UCSC1 ◁ C3

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1617

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×(C11⋊C5)⋊#5997, C3×C11⋊C5×#5997, C3×(C7⋊D7)⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×(C11⋊C5)⋊#5997, C3×C11⋊C5×#5997, C3×(C7⋊D7)⋊AGL(1,𝔽11), …
maximal quotient ofC3×C11⋊C5×C7⋊Dic7, C2×C3×C11⋊C5×C7⋊D7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 64);