Finite Group Databasebeta

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C3×Dic3×C17×C11⋊C5 #46777959

order33660
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic3×C17×C11⋊C5
unambiguous semidirect productC3⋊(C3×C4×C17×C11⋊C5)
unambiguous semidirect product(C11×Dic3)⋊(C3×C5×C17)
unambiguous semidirect product(C3×C11×Dic3)⋊(C5×C17)
unambiguous semidirect product(C11×Dic3×C17)⋊(C3×C5)
unambiguous semidirect product(C3×C11×Dic3×C17)⋊C5

Splittings

derivedC3×C11 ⋊ C3×C4×C5×C17
HallC32×C17×C11⋊C5 ⋊ C4
HallC3×C11×Dic3×C17 ⋊ C5
HallC32×C11×C17 ⋊ C4×C5
HallC32×C11⋊C5 ⋊ C4×C17
HallC3×C11×Dic3 ⋊ C5×C17
HallC11×C17 ⋊ C3×C5×Dic3
HallC32×C17 ⋊ C4×C11⋊C5
HallC32×C11 ⋊ C4×C5×C17
SylowC11 ⋊ C3×C5×Dic3×C17
SylowC32 ⋊ C4×C17×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D3×C11⋊C5
commutator, hypocenterC3×C11C3×C4×C5×C17
FrattiniC2C3×D3×C17×C11⋊C5
Fitting, socleC2×C32×C11×C17C2×C5
prime radicalC2×C32×C17×C11⋊C5C2
cosocleC2×C3×C11C2×C3×C5×C17
LCSG ▷ C3×C11
UCSC1 ◁ C2×C3×C17

112 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 60 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

2142 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 127);