Finite Group Databasebeta

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C32×(C11⋊C5)⋊Dic17 #46777955

order33660
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×(C11⋊C5)⋊Dic17
unambiguous semidirect product(C11⋊C5)⋊(C32×Dic17)
unambiguous semidirect productDic187⋊(C32×C5)
unambiguous semidirect product(C3×Dic187)⋊(C3×C5)
unambiguous semidirect product(C32×Dic187)⋊C5

Splittings

derived, HallC11×C17 ⋊ C32×C4×C5
HallC32×C17×C11⋊C5 ⋊ C4
HallC32×Dic187 ⋊ C5
HallC32×C11×C17 ⋊ C4×C5
HallC17×C11⋊C5 ⋊ C32×C4
HallDic187 ⋊ C32×C5
HallC32×C11⋊C5 ⋊ Dic17
HallC32×C17 ⋊ Dic11⋊C5
HallC32×C11 ⋊ C5×Dic17
HallC11⋊C5 ⋊ C32×Dic17
SylowC17 ⋊ C32×Dic11⋊C5
SylowC11 ⋊ C32×C5×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C32C17⋊AGL(1,𝔽11)
commutator, hypocenterC11×C17C32×C4×C5
FrattiniC2C32×C17⋊AGL(1,𝔽11)
Fitting, socleC2×C32×C11×C17C2×C5
prime radicalC2×C32×C17×C11⋊C5C2
cosocleC2×C11×C17C2×C32×C5
LCSG ▷ C11×C17
UCSC1 ◁ C2×C32

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6732

Conjugacy classes & character table

1206 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 123);