Finite Group Databasebeta

← Prev (#44568775) Next (#44568777) →

C2×C5×D11×#3862 #44568776

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C5×D11×#3862

Splittings

Fitting, socleC2×C5×C72×C11 ⋊ C2×C3
derived, HallC72×C11 ⋊ C22×C3×C5
HallC2×C5×C72×D11 ⋊ C3
HallC5×C11×#3862 ⋊ C22
HallC5×C72×C11 ⋊ C22×C3
HallC2×C72×D11 ⋊ C3×C5
HallC11×#3862 ⋊ C22×C5
HallC5×C72 ⋊ C2×C3×D11
HallC5×C11 ⋊ C22×#3862
SylowC72 ⋊ C2×C3×C5×D11
SylowC11 ⋊ C22×C5×#3862

Subgroups

subgroupG/H
center, hypercenterC2×C5D11×#3862
commutator, cosocle, hypocenterC72×C11C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C72×C11C2×C3
LCSG ▷ C72×C11
UCSC1 ◁ C2×C5

200 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 2310

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 478);