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(C11⋊C5)⋊C16 #11724833

order880
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C5×C16 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C11⋊C5)⋊C16
unambiguous semidirect product(C11⋊C16)⋊C5

Splittings

derived, SylowC11 ⋊ C5×C16
HallC11⋊C16 ⋊ C5
HallC11⋊C5 ⋊ C16

Subgroups

subgroupG/H
center, Frattini, hypercenterC8AGL(1,𝔽11)
commutator, hypocenterC11C5×C16
Fitting, cosocleC8×C11C2×C5
socleC2×C11C5×C8
prime radicalC2×C11⋊C5C8
LCSG ▷ C11
UCSC1 ◁ C8

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Polycyclic presentation:

2,5,2^3,11|a^2=c,c^2=d,d^2=e,f^a=f^10,f^b=f^9

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC16×AGL(1,𝔽11), #66862⋊C5, C2×(C11⋊C5)⋊C16, …
maximal normal subgroup ofC16×AGL(1,𝔽11), #66862⋊C5, C2×(C11⋊C5)⋊C16, …
maximal quotient of(C11⋊C5)⋊C32, C2×(C11⋊C5)⋊C16, #72249058

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 1);