Finite Group Databasebeta

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C2×C11⋊C5×D153 #46777876

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

Aliases

direct productC2×C11⋊C5×D153
unambiguous semidirect product(C2×C9)⋊(D17×C11⋊C5)
unambiguous semidirect product(C2×C17)⋊(D9×C11⋊C5)
unambiguous semidirect product(C2×C11×D153)⋊C5

Splittings

FittingC2×C9×C11×C17 ⋊ C2×C5
derived, HallC9×C11×C17 ⋊ C22×C5
HallC9×C17×C11⋊C5 ⋊ C22
HallC2×C11×D153 ⋊ C5
HallC17×C11⋊C5 ⋊ C2×D9
HallC9×C11⋊C5 ⋊ C2×D17
HallC11×C17 ⋊ C2×C5×D9
HallC9×C17 ⋊ C22×C11⋊C5
HallC9×C11 ⋊ C2×C5×D17
SylowC17 ⋊ C2×D9×C11⋊C5
SylowC11 ⋊ C2×C5×D153
SylowC9 ⋊ C2×D17×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×D153
commutator, cosocle, hypocenterC9×C11×C17C22×C5
FrattiniC3C2×C11⋊C5×D51
FittingC2×C9×C11×C17C2×C5
socleC2×C3×C11×C17C5×D3
LCSG ▷ C9×C11×C17
UCSC1 ◁ C2

120 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, 44);