Finite Group Databasebeta

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C7×D7×D165 #44568870

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

Aliases

direct productC7×D7×D165
unambiguous semidirect product(C3×D7)⋊(C7×D55)
unambiguous semidirect product(C5×D7)⋊(C7×D33)
unambiguous semidirect product(C11×D7)⋊(C7×D15)

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C22
derivedC3×C5×C7×C11 ⋊ C22×C7
HallC5×C72×C11 ⋊ C2×D3
HallC3×C72×C11 ⋊ C2×D5
HallC3×C5×C72 ⋊ C2×D11
HallC72×C11 ⋊ C2×D15
HallC5×C72 ⋊ C2×D33
HallC3×C5×C11 ⋊ C2×C7×D7
HallC3×C72 ⋊ C2×D55
HallC5×C11 ⋊ D3×C7×D7
SylowC72 ⋊ C2×D165
HallC3×C11 ⋊ C7×D5×D7
HallC3×C5 ⋊ C7×D7×D11
SylowC11 ⋊ C7×D7×D15
SylowC5 ⋊ C7×D7×D33
SylowC3 ⋊ C7×D7×D55

Subgroups

subgroupG/H
center, hypercenterC7D7×D165
commutator, cosocle, hypocenterC3×C5×C7×C11C22×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C3×C5×C7×C11
UCSC1 ◁ C7

208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 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

2940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 572);