Finite Group Databasebeta

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#13182656

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

Aliases

No aliases for this group.

Splittings

FittingC5×Q8×C11 ⋊ C4
HallC5×C11 ⋊ #103
SylowC11 ⋊ #4009
SylowC5 ⋊ #66899

Subgroups

subgroupG/H
centerC2C22⋊(C11⋊AGL(1,𝔽5))
commutatorC4×C5×C11C2×C4
FrattiniC4C2×C11⋊AGL(1,𝔽5)
FittingC5×Q8×C11C4
socleC2×C5×C11C22⋊C4
prime radicalC2×D5×C11D4
cosocleC4×D5×C11C22
hypercenterQ8C11⋊AGL(1,𝔽5)
hypocenterC5×C11#103
LCSG ▷ C4×C5×C11 ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ C4 ◁ Q8

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 440

Polycyclic presentation:

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

Conjugacy classes & character table

119 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 465);