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#576×AGL(1,𝔽11) #72269602

order7040
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C29

Aliases

direct product#576×AGL(1,𝔽11)

Splittings

FittingC11×#576 ⋊ C2×C5
HallD11×#576 ⋊ C5
HallC11⋊C5 ⋊ C2×#576
SylowC11 ⋊ C2×C5×#576

Subgroups

subgroupG/H
centerC2C22×D4×AGL(1,𝔽11)
commutator, cosocleC4×C11C25×C5
FrattiniC4C24×AGL(1,𝔽11)
FittingC11×#576C2×C5
socleC2×C11C23×C5×D4
hypercenter#576AGL(1,𝔽11)
hypocenterC11C2×C5×#576
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ #41 ◁ #576

3024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Conjugacy classes & character table

242 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×#3585
maximal normal subgroup ofAGL(1,𝔽11)×#3585

GAP

Past the SmallGroups library coverage — no SmallGroups id.