Finite Group Databasebeta

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C2×#67042⋊C5 #72248809

order3520
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C29

Aliases

direct productC2×#67042⋊C5

Splittings

FittingC2×C11×#41 ⋊ C2×C5
HallC2×#67042 ⋊ C5
HallC11⋊C5 ⋊ C2×H(5,𝔽2)
SylowC11 ⋊ C2×C5×H(5,𝔽2)

Subgroups

subgroupG/H
centerC22C23×AGL(1,𝔽11)
commutator, cosocleC2×C11C25×C5
FrattiniC2C24×AGL(1,𝔽11)
FittingC2×C11×#41C2×C5
socleC22×C11C24×C5
hypercenterC2×#41AGL(1,𝔽11)
hypocenterC11C2×C5×H(5,𝔽2)
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41

1796 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×H(5,𝔽2)×AGL(1,𝔽11), C2×#72222328, C2×#72222331, …
maximal normal subgroup ofC2×H(5,𝔽2)×AGL(1,𝔽11), C2×#72222328, C2×#72222331, …
maximal quotient of#72248961, #72248992, #72254484, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.