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C11⋊C5×C3⋊(C7⋊D7) #30633525

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

Aliases

direct productC11⋊C5×C3⋊(C7⋊D7)
unambiguous semidirect productC3⋊(C11⋊C5×C7⋊D7)
unambiguous semidirect productC7⋊(D21×C11⋊C5)
unambiguous semidirect product(C11×C3⋊(C7⋊D7))⋊C5

Splittings

Fitting, socle, derived, HallC3×C72×C11 ⋊ C2×C5
HallC3×C72×C11⋊C5 ⋊ C2
HallC11×C3⋊(C7⋊D7) ⋊ C5
HallC72×C11⋊C5 ⋊ D3
HallC72×C11 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ C7⋊D7
HallC3×C72 ⋊ C2×C11⋊C5
SylowC72 ⋊ D3×C11⋊C5
HallC3×C11 ⋊ C5×C7⋊D7
SylowC11 ⋊ C5×C3⋊(C7⋊D7)
SylowC3 ⋊ C11⋊C5×C7⋊D7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C72×C11C2×C5
LCSG ▷ C3×C72×C11
UCSC1

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1617

Conjugacy classes & character table

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

Relationships

maximal subgroup of(C7⋊AGL(1,𝔽11))⋊D21, D7×D21×C11⋊C5, AGL(1,𝔽11)×C3⋊(C7⋊D7), …
maximal normal subgroup of(C7⋊AGL(1,𝔽11))⋊D21, D7×D21×C11⋊C5, AGL(1,𝔽11)×C3⋊(C7⋊D7), …
maximal quotient ofC11⋊C5×C3⋊(C7⋊Dic7), C2×C11⋊C5×C3⋊(C7⋊D7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 70);