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C2×C3⋊#11925892 #20300061

order7260
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊#11925892
unambiguous semidirect product(C2×C3)⋊#11925892

Splittings

Fitting, socleC2×C3×C112 ⋊ C2×C5
derived, HallC3×C112 ⋊ C22×C5
HallC3×#10597243 ⋊ C22
HallC2×C3⋊(C11⋊D11) ⋊ C5
Hall#10597243 ⋊ C2×D3
SylowC112 ⋊ C2×C5×D3
SylowC3 ⋊ C2×#11925892

Subgroups

subgroupG/H
center, hypercenterC2C3⋊#11925892
commutator, hypocenterC3×C112C22×C5
FrattiniC1G
Fitting, socleC2×C3×C112C2×C5
LCSG ▷ C3×C112
UCSC1 ◁ C2

280 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C9⋊#11925892, C2×C3⋊(((C11⋊D11)⋊C3)⋊C5), D3×C3⋊#11925892, …
maximal normal subgroup ofC2×C3⋊(((C11⋊D11)⋊C3)⋊C5), C2×C3×C3⋊#11925892, C2×C3⋊((C11⋊C5)⋊AGL(1,𝔽11)), …
maximal quotient ofC2×C9⋊#11925892, D3×C3⋊#11925892, C2×C3×C3⋊#11925892, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 161);