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C2×C5×C3⋊(C11⋊D11) #20300124

order7260
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×C5×C3⋊(C11⋊D11)
unambiguous semidirect product(C2×C3)⋊(C5×C11⋊D11)

Splittings

Fitting, socleC2×C3×C5×C112 ⋊ C2
derived, HallC3×C112 ⋊ C22×C5
HallC3×C5×C112 ⋊ C22
HallC5×C112 ⋊ C2×D3
SylowC112 ⋊ C2×C5×D3
HallC3×C5 ⋊ C2×C11⋊D11
SylowC3 ⋊ C2×C5×C11⋊D11

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊(C11⋊D11)
commutator, hypocenterC3×C112C22×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C112C2
LCSG ▷ C3×C112
UCSC1 ◁ C2×C5

280 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1830 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C9⋊(C11⋊D11), C2×C5×C3⋊((C11⋊D11)⋊C3), C5×D3×C3⋊(C11⋊D11), …
maximal normal subgroup ofC2×C5×C3⋊((C11⋊D11)⋊C3), C2×C3×C5×C3⋊(C11⋊D11), C2×C3⋊#20258402, …
maximal quotient ofC2×C5×C9⋊(C11⋊D11), C5×D3×C3⋊(C11⋊D11), C2×C3×C5×C3⋊(C11⋊D11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 224);