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#13183186

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

Aliases

No aliases for this group.

Splittings

HallC5×C11 ⋊ C4×Q8
SylowC11 ⋊ #4033
SylowC5 ⋊ #66940

Subgroups

subgroupG/H
center, FrattiniC22C22×D55
commutatorC2×C5×C11C22×C4
FittingC5×C11×C4⋊C4C2
socle, prime radical, cosocleC22×C5×C11C23
hypercenterC4⋊C4D55
hypocenterC5×C11C4×Q8
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C22 ◁ C4⋊C4

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1760

Polycyclic presentation:

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

Conjugacy classes & character table

290 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 995);