Finite Group Databasebeta

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C2×C11⋊C5×C3⋊D51 #46778036

order33660
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C11⋊C5×C3⋊D51
unambiguous semidirect product(C2×C3)⋊(C11⋊C5×D51)
unambiguous semidirect product(C2×C17)⋊(C3⋊D3×C11⋊C5)
unambiguous semidirect product(C2×C11×C3⋊D51)⋊C5

Splittings

Fitting, socleC2×C32×C11×C17 ⋊ C2×C5
derived, HallC32×C11×C17 ⋊ C22×C5
HallC32×C17×C11⋊C5 ⋊ C22
HallC2×C11×C3⋊D51 ⋊ C5
HallC17×C11⋊C5 ⋊ C2×C3⋊D3
HallC32×C11⋊C5 ⋊ C2×D17
HallC11×C17 ⋊ C2×C5×C3⋊D3
HallC32×C17 ⋊ C22×C11⋊C5
HallC32×C11 ⋊ C2×C5×D17
SylowC17 ⋊ C2×C3⋊D3×C11⋊C5
SylowC11 ⋊ C2×C5×C3⋊D51
SylowC32 ⋊ C2×D17×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×C3⋊D51
commutator, cosocle, hypocenterC32×C11×C17C22×C5
FrattiniC1G
Fitting, socleC2×C32×C11×C17C2×C5
LCSG ▷ C32×C11×C17
UCSC1 ◁ C2

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3366

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 204);