Finite Group Databasebeta

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C3×C11⋊C5×C3⋊#595 #46778005

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

Aliases

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

Splittings

Fitting, socle, HallC32×C11×C17 ⋊ C4×C5
derivedC3×C11×C17 ⋊ C3×C4×C5
HallC32×C17×C11⋊C5 ⋊ C4
HallC3×C11×C3⋊#595 ⋊ C5
HallC17×C11⋊C5 ⋊ C3×Dic3
HallC32×C11⋊C5 ⋊ #595
HallC11×C17 ⋊ C3×C5×Dic3
HallC32×C17 ⋊ C4×C11⋊C5
HallC32×C11 ⋊ C5×#595
SylowC17 ⋊ C3×Dic3×C11⋊C5
SylowC11 ⋊ C3×C5×C3⋊#595
SylowC32 ⋊ C11⋊C5×#595

Subgroups

subgroupG/H
center, hypercenterC3C11⋊C5×C3⋊#595
commutator, hypocenterC3×C11×C17C3×C4×C5
FrattiniC1G
Fitting, socleC32×C11×C17C4×C5
prime radicalC32×D17×C11⋊C5C2
cosocleC3×C11×D17C2×C3×C5
LCSG ▷ C3×C11×C17
UCSC1 ◁ C3

112 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 42 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) = 1122

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 173);