Finite Group Databasebeta

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C3×C3⋊((C11⋊C5)⋊Dic17) #46777958

order33660
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊((C11⋊C5)⋊Dic17)
unambiguous semidirect productC3⋊(C3×(C11⋊C5)⋊Dic17)
unambiguous semidirect product(C11⋊C5)⋊(C3×Dic51)
unambiguous semidirect productDic561⋊(C3×C5)
unambiguous semidirect product(C3×Dic561)⋊C5

Splittings

derivedC3×C11×C17 ⋊ C3×C4×C5
HallC32×C17×C11⋊C5 ⋊ C4
HallC3×Dic561 ⋊ C5
HallC32×C11×C17 ⋊ C4×C5
HallC17×C11⋊C5 ⋊ C3×Dic3
HallC32×C11⋊C5 ⋊ Dic17
HallC11×C17 ⋊ C3×C5×Dic3
HallC32×C17 ⋊ Dic11⋊C5
HallC32×C11 ⋊ C5×Dic17
HallC11⋊C5 ⋊ C3×Dic51
SylowC17 ⋊ C3×C3⋊(Dic11⋊C5)
SylowC11 ⋊ C3×C5×Dic51
SylowC32 ⋊ (C11⋊C5)⋊Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(C17⋊AGL(1,𝔽11))
commutator, hypocenterC3×C11×C17C3×C4×C5
FrattiniC2C3×C3⋊(C17⋊AGL(1,𝔽11))
Fitting, socleC2×C32×C11×C17C2×C5
prime radicalC2×C32×C17×C11⋊C5C2
cosocleC2×C3×C11×C17C2×C3×C5
LCSG ▷ C3×C11×C17
UCSC1 ◁ C2×C3

112 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2244

Conjugacy classes & character table

1116 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 126);