Finite Group Databasebeta

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C2×C5⋊#10587721 #19129802

order5460
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊#10587721
unambiguous semidirect product(C2×C5)⋊#10587721

Splittings

Fitting, socleC2×C5×C7×C13 ⋊ C2×C3
derived, HallC5×C7×C13 ⋊ C22×C3
HallC2×C13×D35 ⋊ C3
HallC5×#63271 ⋊ C22
Hall#63271 ⋊ C2×D5
HallC2×D35 ⋊ C13⋊C3
HallC7×C13 ⋊ C2×C3×D5
HallC5×C13 ⋊ C2×AGL(1,𝔽7)
HallC5×C7 ⋊ C22×C13⋊C3
SylowC13 ⋊ C2×C5⋊AGL(1,𝔽7)
SylowC7 ⋊ C2×D5×C13⋊C3
SylowC5 ⋊ C2×#10587721

Subgroups

subgroupG/H
center, hypercenterC2C5⋊#10587721
commutator, hypocenterC5×C7×C13C22×C3
FrattiniC1G
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C13⋊C3×C5⋊AGL(1,𝔽7), D3×C5⋊#10587721, C2×C3×C5⋊#10587721, …
maximal normal subgroup ofC2×C13⋊C3×C5⋊AGL(1,𝔽7), C2×C3×C5⋊#10587721, C2×C5×C5⋊#10587721, …
maximal quotient ofC2×C5⋊#13109901, D3×C5⋊#10587721, C2×C3×C5⋊#10587721, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 144);