Finite Group Databasebeta

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C2×#66901⋊C5 #72248877

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

Aliases

direct productC2×#66901⋊C5

Splittings

HallC2×#66901 ⋊ C5
HallC11⋊C5 ⋊ C2×#104
SylowC11 ⋊ C2×C5×#104

Subgroups

subgroupG/H
centerC2×C4C22⋊AGL(1,𝔽11)
commutatorC4×C11C22×C4×C5
FrattiniC2×C4C22×AGL(1,𝔽11)
FittingC2×C11×#41C2×C5
socleC22×C11C5×C22⋊C4
prime radicalC2×#41×C11⋊C5C2
cosocleC2×C4×C11C23×C5
hypercenterC2×#41AGL(1,𝔽11)
hypocenterC11C2×C5×#104
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

340 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 176

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#104×AGL(1,𝔽11), C2×#72222332, C2×#72222328
maximal normal subgroup ofC2×#104×AGL(1,𝔽11), C2×#72222332, C2×#72222328

GAP

Past the SmallGroups library coverage — no SmallGroups id.