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AGL(1,𝔽11)×D165 #49137464

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

Aliases

direct productAGL(1,𝔽11)×D165
unambiguous semidirect productD11⋊(C5×D165)
unambiguous semidirect product(C3×AGL(1,𝔽11))⋊D55
unambiguous semidirect product(C5×AGL(1,𝔽11))⋊D33
unambiguous semidirect product(C11×AGL(1,𝔽11))⋊D15

Splittings

Fitting, socle, derivedC3×C5×C112 ⋊ C22×C5
HallC3×C5×C11×C11⋊C5 ⋊ C22
HallC5×C11×C11⋊C5 ⋊ C2×D3
HallC3×C112 ⋊ C2×C5×D5
SylowC112 ⋊ C2×C5×D15
SylowC3 ⋊ AGL(1,𝔽11)×D55

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C112C22×C5
LCSG ▷ C3×C5×C112
UCSC1

200 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 47 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) = 1650

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 600);