Finite Group Databasebeta

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C2×C3×C11×C5⋊AGL(1,𝔽11) #49137639

order36300
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C11×C5⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C5)⋊(C3×C11×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(C3×D5×C11)
unambiguous semidirect product(C2×D55)⋊(C3×C5×C11)
unambiguous semidirect product(C2×C3×D55)⋊(C5×C11)

Splittings

Fitting, socleC2×C3×C5×C112 ⋊ C2×C5
derivedC5×C11 ⋊ C22×C3×C5×C11
HallC3×C5×C11×C11⋊C5 ⋊ C22
HallC5×C11×C11⋊C5 ⋊ C22×C3
HallC3×C112 ⋊ C2×C5×D5
SylowC112 ⋊ C2×C3×C5×D5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11C5⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC5×C11C22×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C112C2×C5
LCSG ▷ C5×C11
UCSC1 ◁ C2×C3×C11

200 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3300

Conjugacy classes & character table

1650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 775);