Finite Group Databasebeta

← Prev (#44568601) Next (#44568603) →

D7×D21×C11⋊C5 #44568602

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

Aliases

direct productD7×D21×C11⋊C5
unambiguous semidirect product(C3×D7)⋊(D7×C11⋊C5)
unambiguous semidirect product(C7×D7)⋊(D3×C11⋊C5)
unambiguous semidirect product(C11×D7×D21)⋊C5

Splittings

Fitting, socle, derived, HallC3×C72×C11 ⋊ C22×C5
HallC3×C72×C11⋊C5 ⋊ C22
HallC11×D7×D21 ⋊ C5
HallC72×C11⋊C5 ⋊ C2×D3
HallC72×C11 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ D72
HallC3×C72 ⋊ C22×C11⋊C5
SylowC72 ⋊ C2×D3×C11⋊C5
HallC3×C11 ⋊ C5×D72
SylowC11 ⋊ C5×D7×D21
SylowC3 ⋊ D72×C11⋊C5

Subgroups

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

208 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 48 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) = 462

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 304);