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C2×M16×C11⋊C5 #13182602

order1760
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC2×M16×C11⋊C5
unambiguous semidirect product(C2×C11×M16)⋊C5

Splittings

Fitting, HallC2×C11×M16 ⋊ C5
SylowC11 ⋊ C2×C5×M16

Subgroups

subgroupG/H
centerC2×C4C22×C11⋊C5
commutatorC2×C11C22×C4×C5
FrattiniC4C23×C11⋊C5
FittingC2×C11×M16C5
socleC22×C11C2×C4×C5
prime radicalC23×C11⋊C5C4
cosocleC4×C11C23×C5
hypercenterC2×M16C11⋊C5
hypocenterC11C2×C5×M16
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×M16

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 176

A minimal faithful permutation representation — 3 generators on 21 points:

(1,2)(12,13,15,18,17)(14,16,20,21,19);(3,4,5,6,7,8,9,10)(11,12,14,17,13,15,19,21,16,18,20);(4,8)(6,10)

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×M16×C11⋊C5, C2×M16×AGL(1,𝔽11), C2×AGL(1,ℤ/8)×C11⋊C5, …
maximal normal subgroup ofC2×M16×AGL(1,𝔽11), C2×AGL(1,ℤ/8)×C11⋊C5, C2×#66961⋊C5, …
maximal quotient ofD3×M16×C11⋊C5, C4×M16×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 411);