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#100×AGL(1,𝔽11) #72222341

order3520
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct product#100×AGL(1,𝔽11)

Splittings

FittingC11×#100 ⋊ C2×C5
HallD11×#100 ⋊ C5
HallC11⋊C5 ⋊ C2×#100
SylowC11 ⋊ C2×C5×#100

Subgroups

subgroupG/H
centerC2C22⋊C4×AGL(1,𝔽11)
commutatorC22×C11C22×C4×C5
FrattiniC2×C4C22×AGL(1,𝔽11)
FittingC11×#100C2×C5
socleC2×C11C2×C5×C22⋊C4
prime radicalC2×D4×AGL(1,𝔽11)C2
cosocleC2×C4×C11C23×C5
hypercenter#100AGL(1,𝔽11)
hypocenterC11C2×C5×#100
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

372 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

121 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#453×AGL(1,𝔽11), C2×#100×AGL(1,𝔽11)
maximal normal subgroup of#453×AGL(1,𝔽11), C2×#100×AGL(1,𝔽11)
maximal quotient ofC2×#100×AGL(1,𝔽11)

GAP

Past the SmallGroups library coverage — no SmallGroups id.