Finite Group Databasebeta

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C5×D3×D11×C49 #44568387

order32340
automorphism?
homologyAbelianization (H1) = C22×C5×C49 · Schur multiplier (H2) = C2

Aliases

direct productC5×D3×D11×C49

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C22
derived, HallC3×C11 ⋊ C22×C5×C49
HallC5×C11×C49 ⋊ C2×D3
HallC3×C11×C49 ⋊ C22×C5
HallC3×C5×C49 ⋊ C2×D11
HallC11×C49 ⋊ C2×C5×D3
HallC3×C5×C11 ⋊ C22×C49
HallC3×C49 ⋊ C2×C5×D11
HallC5×C11 ⋊ C2×D3×C49
HallC3×C5 ⋊ C2×D11×C49
SylowC11 ⋊ C2×C5×D3×C49
SylowC3 ⋊ C2×C5×D11×C49

Subgroups

subgroupG/H
center, hypercenterC5×C49D3×D11
commutator, hypocenterC3×C11C22×C5×C49
FrattiniC7C5×D3×C7×D11
FittingC3×C5×C11×C49C22
socleC3×C5×C7×C11C22×C7
prime radicalC5×D3×C7×D11C7
cosocleC3×C7×C11C22×C5×C7
LCSG ▷ C3×C11
UCSC1 ◁ C5×C49

120 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

5145 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 89);