Finite Group Databasebeta

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D3×C11⋊C5×C7⋊D7 #44568610

order32340
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C7

Aliases

direct productD3×C11⋊C5×C7⋊D7
unambiguous semidirect product(D3×C7)⋊(D7×C11⋊C5)
unambiguous semidirect product(D3×C11×C7⋊D7)⋊C5

Splittings

Fitting, socle, derived, HallC3×C72×C11 ⋊ C22×C5
HallC3×C72×C11⋊C5 ⋊ C22
HallD3×C11×C7⋊D7 ⋊ C5
HallC72×C11⋊C5 ⋊ C2×D3
HallC72×C11 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×C7⋊D7
HallC3×C72 ⋊ C22×C11⋊C5
SylowC72 ⋊ C2×D3×C11⋊C5
HallC3×C11 ⋊ C2×C5×C7⋊D7
SylowC11 ⋊ C5×D3×C7⋊D7
SylowC3 ⋊ C2×C11⋊C5×C7⋊D7

Subgroups

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

400 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 1617

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 312);