Finite Group Databasebeta

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C22×C5×C11×C49⋊C3 #44568419

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

Aliases

direct productC22×C5×C11×C49⋊C3

Splittings

Fitting, HallC22×C5×C11×C49 ⋊ C3
derived, SylowC49 ⋊ C22×C3×C5×C11
HallC5×C11×C49 ⋊ C22×C3
HallC22×C11×C49 ⋊ C3×C5
HallC22×C5×C49 ⋊ C3×C11
HallC11×C49 ⋊ C22×C3×C5
HallC5×C49 ⋊ C22×C3×C11
HallC22×C49 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC22×C5×C11C49⋊C3
commutator, cosocle, hypocenterC49C22×C3×C5×C11
FrattiniC7C22×C5×C11×ΓL(1,𝔽8)
FittingC22×C5×C11×C49C3
socleC22×C5×C7×C11ΓL(1,𝔽8)
LCSG ▷ C49
UCSC1 ◁ C22×C5×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10780

Conjugacy classes & character table

4180 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 121);