Finite Group Databasebeta

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C2×C3×D3×C11×C11⋊C5 #36345231

order21780
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D3×C11×C11⋊C5
unambiguous semidirect productC3⋊(C22×C3×C11×C11⋊C5)
unambiguous semidirect product(C2×C3)⋊(C2×C3×C11×C11⋊C5)
unambiguous semidirect product(C2×D3×C11)⋊(C3×C5×C11)
unambiguous semidirect product(C2×C3×D3×C11)⋊(C5×C11)

Splittings

Fitting, socleC2×C32×C112 ⋊ C2×C5
derivedC3×C11 ⋊ C22×C3×C5×C11
HallC32×C11×C11⋊C5 ⋊ C22
HallC2×C3×D3×C112 ⋊ C5
HallC32×C112 ⋊ C22×C5
SylowC112 ⋊ C2×C3×C5×D3
SylowC32 ⋊ C22×C11×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D3×C11⋊C5
commutator, cosocle, hypocenterC3×C11C22×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C32×C112C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C2×C3×C11

220 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 84 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

1386 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 580);