Finite Group Databasebeta

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C3×C3⋊(C11⋊#66772) #46778095

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

Aliases

direct productC3×C3⋊(C11⋊#66772)
unambiguous semidirect productC3⋊(C3×C11⋊#66772)
unambiguous semidirect productC11⋊(C3×C3⋊#66772)

Splittings

Fitting, socle, HallC32×C5×C11×C17 ⋊ C4
derivedC3×C5×C11×C17 ⋊ C3×C4
HallC32×C11×C17 ⋊ Dic5
HallC5×C11×C17 ⋊ C3×Dic3
HallC32×C5×C17 ⋊ Dic11
HallC32×C5×C11 ⋊ #595
HallC11×C17 ⋊ C3×Dic15
HallC32×C17 ⋊ Dic55
HallC32×C11 ⋊ #66772
HallC5×C17 ⋊ C3×Dic33
HallC5×C11 ⋊ C3×C3⋊#595
HallC32×C5 ⋊ C11⋊#595
SylowC17 ⋊ C3×Dic165
SylowC11 ⋊ C3×C3⋊#66772
SylowC32 ⋊ C11⋊#66772
SylowC5 ⋊ C3×C3⋊(C11⋊#595)

Subgroups

subgroupG/H
center, hypercenterC3C3⋊(C11⋊#66772)
commutator, hypocenterC3×C5×C11×C17C3×C4
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC32×C5×C11×D17C2
cosocleC3×C5×C11×D17C2×C3
LCSG ▷ C3×C5×C11×C17
UCSC1 ◁ C3

112 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 5610

Conjugacy classes & character table

2484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 263);