Finite Group Databasebeta

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C7⋊D7×D165 #44568882

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

Aliases

direct productC7⋊D7×D165

Splittings

Fitting, socle, derived, HallC3×C5×C72×C11 ⋊ C22
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 ⋊ D5×C7⋊D7
HallC3×C5 ⋊ D11×C7⋊D7
SylowC11 ⋊ D15×C7⋊D7
SylowC5 ⋊ D33×C7⋊D7
SylowC3 ⋊ C7⋊D7×D55

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C72×C11C22
LCSG ▷ C3×C5×C72×C11
UCSC1

400 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 100 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

2184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 584);