Finite Group Databasebeta

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C32×D5×C11×D11 #36345295

order21780
automorphism?
homologyAbelianization (H1) = C22×C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC32×D5×C11×D11
unambiguous semidirect product(D5×C11)⋊(C2×C32×C11)
unambiguous semidirect product(C5×D11)⋊(C2×C32×C11)
unambiguous semidirect productD55⋊(C2×C32×C11)

Splittings

Fitting, socle, HallC32×C5×C112 ⋊ C22
derivedC5×C11 ⋊ C22×C32×C11
HallC32×C112 ⋊ C2×D5
HallC5×C112 ⋊ C22×C32
SylowC112 ⋊ C2×C32×D5
HallC32×C5 ⋊ C2×C11×D11
SylowC5 ⋊ C2×C32×C11×D11

Subgroups

subgroupG/H
center, hypercenterC32×C11D5×D11
commutator, cosocle, hypocenterC5×C11C22×C32×C11
FrattiniC1G
Fitting, socleC32×C5×C112C22
LCSG ▷ C5×C11
UCSC1 ◁ C32×C11

360 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 120 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

2772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 644);