Finite Group Databasebeta

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C72×D11×D15 #44568867

order32340
automorphism?
homologyAbelianization (H1) = C22×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC72×D11×D15
unambiguous semidirect product(C3×D11)⋊(C72×D5)
unambiguous semidirect product(C5×D11)⋊(D3×C72)

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C22
derived, HallC3×C5×C11 ⋊ C22×C72
HallC5×C72×C11 ⋊ C2×D3
HallC3×C72×C11 ⋊ C2×D5
HallC3×C5×C72 ⋊ C2×D11
HallC72×C11 ⋊ C2×D15
HallC5×C72 ⋊ D3×D11
HallC3×C72 ⋊ D5×D11
HallC5×C11 ⋊ C2×D3×C72
HallC3×C11 ⋊ C2×C72×D5
HallC3×C5 ⋊ C2×C72×D11
SylowC11 ⋊ C2×C72×D15
SylowC5 ⋊ D3×C72×D11
SylowC3 ⋊ C72×D5×D11

Subgroups

subgroupG/H
center, hypercenterC72D11×D15
commutator, cosocle, hypocenterC3×C5×C11C22×C72
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C3×C5×C11
UCSC1 ◁ C72

400 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 160 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

3087 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 569);