Finite Group Databasebeta

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C2×C11×C3⋊D21 #14583946

order2772
isoclinismisoclinic class of C3⋊D21
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C11×C3⋊D21
unambiguous semidirect product(C2×C3)⋊(C11×D21)
unambiguous semidirect product(C2×C7)⋊(C11×C3⋊D3)

Splittings

Fitting, socleC2×C32×C7×C11 ⋊ C2
derived, HallC32×C7 ⋊ C22×C11
HallC32×C7×C11 ⋊ C22
HallC32×C11 ⋊ C2×D7
HallC7×C11 ⋊ C2×C3⋊D3
SylowC32 ⋊ C2×C11×D7
SylowC7 ⋊ C2×C11×C3⋊D3

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊D21
commutator, cosocle, hypocenterC32×C7C22×C11
FrattiniC1G
Fitting, socleC2×C32×C7×C11C2
LCSG ▷ C32×C7
UCSC1 ◁ C2×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1386

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C11⋊C5×C3⋊D21, D5×C11×C3⋊D21, C2×C11×C3⋊D105, …
maximal normal subgroup ofC2×C11⋊C5×C3⋊D21, C2×C5×C11×C3⋊D21, C2×C7×C11×C3⋊D21, …
maximal quotient ofD5×C11×C3⋊D21, C2×C11×C3⋊D105, C2×C5×C11×C3⋊D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2772, 102);