Finite Group Databasebeta

C32×D4×C22⋊A4 #72253044

order3456
automorphism?
homologyAbelianization (H1) = C22×C33 · Schur multiplier (H2) = C25×C33

Aliases

direct productC32×D4×C22⋊A4

Splittings

FittingC24×C32×D4 ⋊ C3
SylowC24×D4 ⋊ C33

Subgroups

subgroupG/H
centerC2×C32C22×C22⋊A4
commutator, cosocleC25C22×C33
FrattiniC2C22×C32×C22⋊A4
FittingC24×C32×D4C3
socleC25×C32C22×C3
hypercenterC32×D4C22⋊A4
hypocenterC24C33×D4
LCSG ▷ C25 ▷ C24
UCSC1 ◁ C2×C32 ◁ C32×D4

12008 conjugacy classes of subgroups; only the 384 normal subgroups are shown.

normal subgroups only

This group has 12008 conjugacy classes of subgroups — too many to draw. Only its 384 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) = 216

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.