Finite Group Databasebeta

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C3×C11×Dic165 #36345034

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

Aliases

direct productC3×C11×Dic165
unambiguous semidirect productC3⋊(C3×C11×Dic55)
unambiguous semidirect productC11⋊(C3×C11×Dic15)

Splittings

derivedC3×C5×C11 ⋊ C3×C4×C11
HallC32×C5×C112 ⋊ C4
HallC32×C112 ⋊ Dic5
HallC5×C112 ⋊ C3×Dic3
SylowC112 ⋊ C3×Dic15
HallC32×C5 ⋊ C11×Dic11
SylowC32 ⋊ C11×Dic55
SylowC5 ⋊ C3×C11×Dic33

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D165
commutator, hypocenterC3×C5×C11C3×C4×C11
FrattiniC2C3×C11×D165
Fitting, socle, prime radicalC2×C32×C5×C112C2
cosocleC2×C3×C5×C11C2×C3×C11
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2×C3×C11

232 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 68 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

5544 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 383);