Finite Group Databasebeta

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C3×D55⋊(C7⋊D7) #44568836

order32340
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C7

Aliases

direct productC3×D55⋊(C7⋊D7)
unambiguous semidirect productD55⋊(C3×C7⋊D7)

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C22
derived, HallC5×C72×C11 ⋊ C22×C3
HallC3×C72×C11 ⋊ C2×D5
HallC3×C5×C72 ⋊ C2×D11
HallC72×C11 ⋊ C2×C3×D5
HallC5×C72 ⋊ C2×C3×D11
HallC3×C5×C11 ⋊ C2×C7⋊D7
HallC3×C72 ⋊ D5×D11
HallC5×C11 ⋊ C2×C3×C7⋊D7
SylowC72 ⋊ C3×D5×D11
HallC3×C11 ⋊ D5×C7⋊D7
HallC3×C5 ⋊ D11×C7⋊D7
SylowC11 ⋊ C3×D5×C7⋊D7
SylowC5 ⋊ C3×D11×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC3D55⋊(C7⋊D7)
commutator, cosocle, hypocenterC5×C72×C11C22×C3
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C5×C72×C11
UCSC1 ◁ C3

400 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 110 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

2172 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 538);