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#4325⋊C5 #11724852

order880
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product#4325⋊C5

Splittings

FittingQ8×C11 ⋊ C2×C5
Hall#4325 ⋊ C5
HallC11⋊C5 ⋊ SD16
SylowC11 ⋊ C5×SD16

Subgroups

subgroupG/H
centerC2C22⋊AGL(1,𝔽11)
commutator, cosocleC4×C11C22×C5
FrattiniC4C2×AGL(1,𝔽11)
FittingQ8×C11C2×C5
socleC2×C11C5×D4
prime radicalC4⋊AGL(1,𝔽11)C2
hypercenterQ8AGL(1,𝔽11)
hypocenterC11C5×SD16
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C4 ◁ Q8

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 88

Polycyclic presentation:

2^2,5,2^2,11|b^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^10,d^b=de,f^c=f^9

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofSD16×AGL(1,𝔽11), #66967⋊C5, #66971⋊C5, …
maximal normal subgroup ofSD16×AGL(1,𝔽11), #66967⋊C5, #66971⋊C5, …
maximal quotient of#66872⋊C5, #66873⋊C5, #66899⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 20);