Finite Group Databasebeta

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C82×AGL(1,𝔽11) #72249010

order7040
automorphism?
homologyAbelianization (H1) = C2×C5×C82 · Schur multiplier (H2) = C22×C8

Aliases

direct productC82×AGL(1,𝔽11)

Splittings

FittingC82×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C5×C82
HallC82×D11 ⋊ C5
HallC11⋊C5 ⋊ C2×C82

Subgroups

subgroupG/H
center, hypercenterC82AGL(1,𝔽11)
commutator, hypocenterC11C2×C5×C82
FrattiniC42C22×AGL(1,𝔽11)
FittingC82×C11C2×C5
socleC22×C11C2×C42×C5
prime radicalC22×AGL(1,𝔽11)C42
cosocleC42×C11C23×C5
LCSG ▷ C11
UCSC1 ◁ C82

560 conjugacy classes of subgroups; only the 317 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 317 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) = 704

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽11)×#1712, AGL(1,𝔽11)×#1705, AGL(1,𝔽11)×#1455
maximal normal subgroup ofAGL(1,𝔽11)×#1712, AGL(1,𝔽11)×#1705, AGL(1,𝔽11)×#1455

GAP

Past the SmallGroups library coverage — no SmallGroups id.