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#10587721⋊D11 #26046473

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

Aliases

unambiguous semidirect product#10587721⋊D11

Splittings

Fitting, socle, derived, HallC7×C11×C13 ⋊ C22×C3
HallD7×D143 ⋊ C3
HallC11×#63271 ⋊ C22
Hall#63271 ⋊ C2×D11
HallC11×C13 ⋊ C2×AGL(1,𝔽7)
HallC7×C13 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×D13⋊C3
SylowC13 ⋊ D11×AGL(1,𝔽7)
SylowC11 ⋊ #10587717⋊C2
SylowC7 ⋊ C2×C11⋊(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|e^a=e^10,f^a=f^12,d^b=d^6,d^c=d^2,f^c=f^9

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×C11⋊(D13⋊C3), C3×#10587721⋊D11, #49114703, …
maximal normal subgroup ofAGL(1,𝔽7)×C11⋊(D13⋊C3), C3×#10587721⋊D11
maximal quotient of#13109901⋊D11, C3×#10587721⋊D11, #49114703, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 63);