Finite Group Databasebeta

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C2×C5×C11×D153 #46777944

order33660
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

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

Splittings

FittingC2×C5×C9×C11×C17 ⋊ C2
derived, HallC9×C17 ⋊ C22×C5×C11
HallC5×C9×C11×C17 ⋊ C22
HallC9×C11×C17 ⋊ C22×C5
HallC5×C11×C17 ⋊ C2×D9
HallC5×C9×C17 ⋊ C22×C11
HallC5×C9×C11 ⋊ C2×D17
HallC11×C17 ⋊ C2×C5×D9
HallC9×C11 ⋊ C2×C5×D17
HallC5×C17 ⋊ C2×C11×D9
HallC5×C9 ⋊ C2×C11×D17
SylowC17 ⋊ C2×C5×C11×D9
SylowC9 ⋊ C2×C5×C11×D17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D153
commutator, cosocle, hypocenterC9×C17C22×C5×C11
FrattiniC3C2×C5×C11×D51
FittingC2×C5×C9×C11×C17C2
socleC2×C3×C5×C11×C17D3
LCSG ▷ C9×C17
UCSC1 ◁ C2×C5×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16830

Conjugacy classes & character table

8580 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 112);