Finite Group Databasebeta

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C2×C3×C5×C11×D49 #44568423

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×C11×D49

Splittings

FittingC2×C3×C5×C11×C49 ⋊ C2
derived, SylowC49 ⋊ C22×C3×C5×C11
HallC3×C5×C11×C49 ⋊ C22
HallC5×C11×C49 ⋊ C22×C3
HallC3×C11×C49 ⋊ C22×C5
HallC3×C5×C49 ⋊ C22×C11
HallC11×C49 ⋊ C22×C3×C5
HallC5×C49 ⋊ C22×C3×C11
HallC3×C49 ⋊ C22×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C11D49
commutator, cosocle, hypocenterC49C22×C3×C5×C11
FrattiniC7C2×C3×C5×C11×D7
FittingC2×C3×C5×C11×C49C2
socleC2×C3×C5×C7×C11D7
LCSG ▷ C49
UCSC1 ◁ C2×C3×C5×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16170

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(32340, 125);