Finite Group Databasebeta

← Prev (#44568712) Next (#44568714) →

D5×D11×#3861 #44568713

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

Aliases

direct productD5×D11×#3861
unambiguous semidirect product(D5×C11)⋊(C2×#3861)
unambiguous semidirect product(C5×D11)⋊(C2×#3861)
unambiguous semidirect productD55⋊(C2×#3861)

Splittings

Fitting, socle, derived, HallC5×C72×C11 ⋊ C22×C3
HallC72×D5×D11 ⋊ C3
HallC5×C11×#3861 ⋊ C22
HallC11×#3861 ⋊ C2×D5
HallC5×#3861 ⋊ C2×D11
HallC72×C11 ⋊ C2×C3×D5
HallC5×C72 ⋊ C2×C3×D11
HallC5×C11 ⋊ C22×#3861
SylowC72 ⋊ C3×D5×D11
SylowC11 ⋊ C2×D5×#3861
SylowC5 ⋊ C2×D11×#3861

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C11C22×C3
LCSG ▷ C5×C72×C11
UCSC1

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) = 2695

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 415);