Finite Group Databasebeta

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C3×D72×C11⋊C5 #44568589

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

Aliases

direct productC3×D72×C11⋊C5
unambiguous semidirect product(C3×C11×D72)⋊C5

Splittings

Fitting, socle, HallC3×C72×C11 ⋊ C22×C5
derived, HallC72×C11 ⋊ C22×C3×C5
HallC3×C72×C11⋊C5 ⋊ C22
HallC3×C11×D72 ⋊ C5
HallC72×C11⋊C5 ⋊ C22×C3
HallC11×D72 ⋊ C3×C5
HallC3×C72 ⋊ C22×C11⋊C5
SylowC72 ⋊ C22×C3×C11⋊C5
HallC3×C11 ⋊ C5×D72
SylowC11 ⋊ C3×C5×D72

Subgroups

subgroupG/H
center, hypercenterC3D72×C11⋊C5
commutator, cosocle, hypocenterC72×C11C22×C3×C5
FrattiniC1G
Fitting, socleC3×C72×C11C22×C5
LCSG ▷ C72×C11
UCSC1 ◁ C3

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) = 462

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 291);