Finite Group Databasebeta

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D3×D15×C121 #36344751

order21780
automorphism?
homologyAbelianization (H1) = C22×C121 · Schur multiplier (H2) = C2

Aliases

direct productD3×D15×C121
unambiguous semidirect product(C3×D3)⋊(D5×C121)
unambiguous semidirect product(C5×D3)⋊(D3×C121)

Splittings

Fitting, HallC32×C5×C121 ⋊ C22
derived, HallC32×C5 ⋊ C22×C121
HallC32×C121 ⋊ C2×D5
HallC5×C121 ⋊ D32
SylowC32 ⋊ C2×D5×C121
SylowC5 ⋊ D32×C121

Subgroups

subgroupG/H
center, hypercenterC121D3×D15
commutator, hypocenterC32×C5C22×C121
FrattiniC11D3×C11×D15
FittingC32×C5×C121C22
socle, cosocleC32×C5×C11C22×C11
prime radicalD3×C11×D15C11
LCSG ▷ C32×C5
UCSC1 ◁ C121

132 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 48 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

3267 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 100);