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C11×#4009 #13182631

order1760
automorphism?
homologyAbelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×#4009

Splittings

FittingC5×Q8×C11 ⋊ C4
HallC5×C11 ⋊ #103
SylowC5 ⋊ C11×#103

Subgroups

subgroupG/H
centerC2×C11C22⋊AGL(1,𝔽5)
commutatorC4×C5C2×C4×C11
FrattiniC4C2×C11×AGL(1,𝔽5)
FittingC5×Q8×C11C4
socleC2×C5×C11C22⋊C4
prime radicalC2×D5×C11D4
cosocleC4×D5C22×C11
hypercenterQ8×C11AGL(1,𝔽5)
hypocenterC5C11×#103
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C11 ◁ C4×C11 ◁ Q8×C11

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,16,15)(17,18,20,22)(19,24,23,21);(13,14,15,16)(18,21)(19,23)(22,24)

Conjugacy classes & character table

209 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 440);