Finite Group Databasebeta

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C2×C7×C3⋊(C11⋊D11) #23779081

order10164
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×C7×C3⋊(C11⋊D11)
unambiguous semidirect product(C2×C3)⋊(C7×C11⋊D11)
unambiguous semidirect product(C2×C11)⋊(C7×D33)

Splittings

Fitting, socleC2×C3×C7×C112 ⋊ C2
derived, HallC3×C112 ⋊ C22×C7
HallC3×C7×C112 ⋊ C22
HallC7×C112 ⋊ C2×D3
SylowC112 ⋊ C2×D3×C7
HallC3×C7 ⋊ C2×C11⋊D11
SylowC3 ⋊ C2×C7×C11⋊D11

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(C11⋊D11)
commutator, cosocle, hypocenterC3×C112C22×C7
FrattiniC1G
Fitting, socleC2×C3×C7×C112C2
LCSG ▷ C3×C112
UCSC1 ◁ C2×C7

280 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2562 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C9⋊(C11⋊D11), C2×C7×C3⋊((C11⋊D11)⋊C3), C2×C3⋊((C11⋊D11)⋊ΓL(1,𝔽8)), …
maximal normal subgroup ofC2×C7×C3⋊((C11⋊D11)⋊C3), C2×C3⋊((C11⋊D11)⋊ΓL(1,𝔽8)), C2×ΓL(1,𝔽8)×C3⋊(C11⋊D11), …
maximal quotient ofC2×C7×C9⋊(C11⋊D11), D3×C7×C3⋊(C11⋊D11), C2×C3×C7×C3⋊(C11⋊D11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10164, 133);