Finite Group Databasebeta

← Prev (#46778076) Next (#46778078) →

C3×C5×C11×C3⋊#595 #46778077

order33660
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11×C3⋊#595
unambiguous semidirect productC3⋊(C3×C5×C11×#595)

Splittings

Fitting, socle, HallC32×C5×C11×C17 ⋊ C4
derivedC3×C17 ⋊ C3×C4×C5×C11
HallC32×C11×C17 ⋊ C4×C5
HallC5×C11×C17 ⋊ C3×Dic3
HallC32×C5×C17 ⋊ C4×C11
HallC32×C5×C11 ⋊ #595
HallC11×C17 ⋊ C3×C5×Dic3
HallC32×C17 ⋊ C4×C5×C11
HallC32×C11 ⋊ C5×#595
HallC5×C17 ⋊ C3×C11×Dic3
HallC32×C5 ⋊ C11×#595
SylowC17 ⋊ C3×C5×C11×Dic3
SylowC32 ⋊ C5×C11×#595

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11C3⋊#595
commutator, hypocenterC3×C17C3×C4×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC32×C5×C11×D17C2
cosocleC3×D17C2×C3×C5×C11
LCSG ▷ C3×C17
UCSC1 ◁ C3×C5×C11

112 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 56 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

2970 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 245);