Finite Group Databasebeta

C2×C3×(C2×D9)⋊C8 #13143092

order1728
isoclinismisoclinic class of Dic18
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C3×(C2×D9)⋊C8

Splittings

FittingC22×C3×C8×C9 ⋊ C2
SylowC3×C9 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC22×C3×C4C2×D9
commutatorC2×C9C22×C3×C8
FrattiniC2×C3×C4C22×C3×D3
FittingC22×C3×C8×C9C2
socleC23×C32C4×D3
prime radicalC23×C3×D9C4
cosocleC2×C4×C9C23×C3
hypercenterC22×C3×C8D9
hypocenterC9C2×C3×C22⋊C8
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C3×C4 ◁ C22×C3×C8

682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 9155);