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#10587716⋊D11 #26046483

order12012
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product#10587716⋊D11

Splittings

Fitting, socle, derived, HallC7×C11×C13 ⋊ C22×C3
HallD13×D77 ⋊ C3
HallC11×#63270 ⋊ C22
Hall#63270 ⋊ C2×D11
HallC11×C13 ⋊ C2×AGL(1,𝔽7)
HallC7×C13 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×D13⋊C3
SylowC13 ⋊ C2×C11⋊AGL(1,𝔽7)
SylowC11 ⋊ #10587716⋊C2
SylowC7 ⋊ D11×D13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C13C22×C3
LCSG ▷ C7×C11×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,3,7,11,13|f^a=f^12,d^b=d^6,e^b=e^10,d^c=d^2,f^c=f^3

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13⋊C3×C11⋊AGL(1,𝔽7), C3×#10587716⋊D11, #10587716⋊D33, …
maximal normal subgroup ofD13⋊C3×C11⋊AGL(1,𝔽7), C3×#10587716⋊D11
maximal quotient of#13109896⋊D11, C3×#10587716⋊D11, #10587716⋊D33, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 73);