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(C11⋊C5)⋊D11 #11925899

order1210
isoclinismisoclinic class of (C11⋊C5)⋊D11
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C11⋊C5)⋊D11

Splittings

Fitting, socle, derived, SylowC112 ⋊ C2×C5
HallC11×C11⋊C5 ⋊ C2
HallC11⋊D11 ⋊ C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC112C2×C5
LCSG ▷ C112
UCSC1

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 55

Polycyclic presentation:

2,5,11^2|c^a=c^10,d^a=d^10,c^b=c^4

Conjugacy classes & character table

46 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×AGL(1,𝔽11), C2×(C11⋊C5)⋊D11, C3×(C11⋊C5)⋊D11, …
maximal normal subgroup ofD11×AGL(1,𝔽11), C2×(C11⋊C5)⋊D11, C3×(C11⋊C5)⋊D11, …
maximal quotient of(C11⋊C5)⋊Dic11, C2×(C11⋊C5)⋊D11, C3×(C11⋊C5)⋊D11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1210, 16);