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#13182652

order1760
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C23

Aliases

No aliases for this group.

Splittings

FittingC2×C4×C5×C11 ⋊ C4
HallC5×C11 ⋊ #95
SylowC11 ⋊ (C2×AGL(1,𝔽5))⋊C4
SylowC5 ⋊ C11⋊#95

Subgroups

subgroupG/H
center, FrattiniC22C2×C11⋊AGL(1,𝔽5)
commutatorC2×C5×C11C42
FittingC2×C4×C5×C11C4
socleC22×C5×C11C2×C4
prime radical, cosocleC22×D5×C11C22
hypercenterC2×C4C11⋊AGL(1,𝔽5)
hypocenterC5×C11#95
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C22 ◁ C2×C4

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 440

Polycyclic presentation:

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

Conjugacy classes & character table

188 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 461);