Finite Group Databasebeta

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C3×C5×(C7⋊D7)⋊D11 #44568807

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

Aliases

direct productC3×C5×(C7⋊D7)⋊D11

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C22
derived, HallC72×C11 ⋊ C22×C3×C5
HallC5×C72×C11 ⋊ C22×C3
HallC3×C72×C11 ⋊ C22×C5
HallC3×C5×C72 ⋊ C2×D11
HallC5×C72 ⋊ C2×C3×D11
HallC3×C5×C11 ⋊ D72
HallC3×C72 ⋊ C2×C5×D11
HallC5×C11 ⋊ C3×D72
SylowC72 ⋊ C2×C3×C5×D11
HallC3×C11 ⋊ C5×D72
SylowC11 ⋊ C3×C5×D72

Subgroups

subgroupG/H
center, hypercenterC3×C5(C7⋊D7)⋊D11
commutator, cosocle, hypocenterC72×C11C22×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C72×C11
UCSC1 ◁ C3×C5

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

normal subgroups only

This group has 208 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) = 2310

Conjugacy classes & character table

2325 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 509);