Finite Group Databasebeta

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#518×AGL(1,𝔽11) #72269466

order7040
automorphism?
homologyAbelianization (H1) = C24×C4×C5 · Schur multiplier (H2) = C29

Aliases

direct product#518×AGL(1,𝔽11)

Splittings

FittingC11×#518 ⋊ C2×C5
HallD11×#518 ⋊ C5
HallC11⋊C5 ⋊ C2×#518
SylowC11 ⋊ C2×C5×#518

Subgroups

subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽11)
commutatorC2×C11C24×C4×C5
FittingC11×#518C2×C5
socle, cosocleC22×C11C25×C5
prime radicalC22×D4×AGL(1,𝔽11)C2
hypercenter#518AGL(1,𝔽11)
hypocenterC11C2×C5×#518
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #518

3840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.