Finite Group Databasebeta

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C2×C3×C3⋊(C5⋊(C11⋊D11)) #36345384

order21780
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×C3×C3⋊(C5⋊(C11⋊D11))
unambiguous semidirect product(C2×C3)⋊(C3×C5⋊(C11⋊D11))
unambiguous semidirect product(C2×C5)⋊(C3×C3⋊(C11⋊D11))
unambiguous semidirect product(C2×C11)⋊(C3×D165)

Splittings

Fitting, socleC2×C32×C5×C112 ⋊ C2
derivedC3×C5×C112 ⋊ C22×C3
HallC32×C5×C112 ⋊ C22
HallC32×C112 ⋊ C2×D5
HallC5×C112 ⋊ C2×C3×D3
SylowC112 ⋊ C2×C3×D15
HallC32×C5 ⋊ C2×C11⋊D11
SylowC32 ⋊ C2×C5⋊(C11⋊D11)
SylowC5 ⋊ C2×C3×C3⋊(C11⋊D11)

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(C5⋊(C11⋊D11))
commutator, cosocle, hypocenterC3×C5×C112C22×C3
FrattiniC1G
Fitting, socleC2×C32×C5×C112C2
LCSG ▷ C3×C5×C112
UCSC1 ◁ C2×C3

616 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

5454 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 733);