Finite Group Databasebeta

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D11×C3⋊(C5⋊(C7⋊D7)) #44568880

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

Aliases

direct productD11×C3⋊(C5⋊(C7⋊D7))
unambiguous semidirect product(C3×D11)⋊(C5⋊(C7⋊D7))
unambiguous semidirect product(C5×D11)⋊(C3⋊(C7⋊D7))
unambiguous semidirect product(C7×D11)⋊D105

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 ⋊ D3×D11
HallC3×C5×C11 ⋊ C2×C7⋊D7
HallC3×C72 ⋊ D5×D11
HallC5×C11 ⋊ C2×C3⋊(C7⋊D7)
SylowC72 ⋊ D11×D15
HallC3×C11 ⋊ C2×C5⋊(C7⋊D7)
HallC3×C5 ⋊ D11×C7⋊D7
SylowC11 ⋊ C2×C3⋊(C5⋊(C7⋊D7))
SylowC5 ⋊ D11×C3⋊(C7⋊D7)
SylowC3 ⋊ D11×C5⋊(C7⋊D7)

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 124 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 124 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

2583 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 582);