Finite Group Databasebeta

C2×A4×C32⋊C9 #14518362

order1944
automorphism?
homologyAbelianization (H1) = C2×C32×C9 · Schur multiplier (H2) = C2×C34

Aliases

direct productC2×A4×C32⋊C9

Splittings

FittingC23×C32⋊C9 ⋊ C3
SylowC23 ⋊ C3×C32⋊C9

Subgroups

subgroupG/H
centerC2×C32C32×A4
commutatorC22×C3C2×C32×C9
FrattiniC32C2×C32×A4
FittingC23×C32⋊C9C3
socleC23×C32C33
prime radicalC2×C33×A4C3
cosocleC22×C32C2×C33
hypercenterC2×C32⋊C9A4
hypocenterC22C2×C3×C32⋊C9
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C2×C32 ◁ C2×C32⋊C9

668 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 172 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) = 162

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2756);