Finite Group Databasebeta

← Prev (#36344981) Next (#36344983) →

C3×C11×Dic3×C11⋊C5 #36344982

order21780
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×Dic3×C11⋊C5
unambiguous semidirect productC3⋊(C3×C4×C11×C11⋊C5)
unambiguous semidirect product(C11×Dic3)⋊(C3×C5×C11)
unambiguous semidirect product(C3×C11×Dic3)⋊(C5×C11)

Splittings

derivedC3×C11 ⋊ C3×C4×C5×C11
HallC32×C11×C11⋊C5 ⋊ C4
HallC3×C112×Dic3 ⋊ C5
HallC32×C112 ⋊ C4×C5
SylowC112 ⋊ C3×C5×Dic3
SylowC32 ⋊ C4×C11×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D3×C11⋊C5
commutator, hypocenterC3×C11C3×C4×C5×C11
FrattiniC2C3×D3×C11×C11⋊C5
Fitting, socleC2×C32×C112C2×C5
prime radicalC2×C32×C11×C11⋊C5C2
cosocleC2×C3×C11C2×C3×C5×C11
LCSG ▷ C3×C11
UCSC1 ◁ C2×C3×C11

140 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 60 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, 331);