Finite Group Databasebeta

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C4×#41×C11⋊C5 #72248938

order3520
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC4×#41×C11⋊C5

Splittings

Fitting, HallC4×C11×#41 ⋊ C5
SylowC11 ⋊ C4×C5×#41

Subgroups

subgroupG/H
centerC42C22×C11⋊C5
commutatorC2×C11C23×C4×C5
FrattiniC22C24×C11⋊C5
FittingC4×C11×#41C5
socle, cosocleC22×C11C24×C5
prime radicalC2×#41×C11⋊C5C2
hypercenterC4×#41C11⋊C5
hypocenterC11C4×C5×#41
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C42 ◁ C4×#41

620 conjugacy classes of subgroups; only the 375 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 375 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) = 352

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11⋊C5×#3498, C4×#41×AGL(1,𝔽11), #72254484
maximal normal subgroup ofC11⋊C5×#3498, C4×#41×AGL(1,𝔽11), #72254484

GAP

Past the SmallGroups library coverage — no SmallGroups id.