Finite Group Databasebeta

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C3×C11×Dic3×C17 #20269666

order6732
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C3×C4×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×Dic3×C17
unambiguous semidirect productC3⋊(C3×C4×C11×C17)

Splittings

derivedC3 ⋊ C3×C4×C11×C17
HallC32×C11×C17 ⋊ C4
HallC32×C17 ⋊ C4×C11
HallC32×C11 ⋊ C4×C17
SylowC32 ⋊ C4×C11×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11×C17D3
commutator, hypocenterC3C3×C4×C11×C17
FrattiniC2C3×D3×C11×C17
Fitting, socleC2×C32×C11×C17C2
LCSG ▷ C3
UCSC1 ◁ C2×C3×C11×C17

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3366 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×Dic3×C17×C11⋊C5, C3×C11×C17×Dic15, C3×C5×C11×Dic3×C17, …
maximal normal subgroup ofC3×Dic3×C17×C11⋊C5, C3×C5×C11×Dic3×C17
maximal quotient ofC3×C11×C17×Dic15, C3×C5×C11×Dic3×C17, C3×C11×C17×ΓL(1,𝔽16)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6732, 33);