Finite Group Databasebeta

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#13182657

order1760
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C22

Aliases

No aliases for this group.

Splittings

FittingC23×C5×C11 ⋊ C4
HallC5×C11 ⋊ #99
SylowC11 ⋊ #4011
SylowC5 ⋊ #66898

Subgroups

subgroupG/H
centerC2C22⋊(C11⋊AGL(1,𝔽5))
commutatorC22×C5×C11C2×C4
FrattiniC22C2×C11⋊AGL(1,𝔽5)
FittingC23×C5×C11C4
socleC2×C5×C11C22⋊C4
prime radicalC2×C11×C22⋊D5C2
cosocleC22×D5×C11C22
hypercenterC23C11⋊AGL(1,𝔽5)
hypocenterC5×C11#99
LCSG ▷ C22×C5×C11 ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ C22 ◁ C23

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 440

Polycyclic presentation:

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

Conjugacy classes & character table

149 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 466);