Finite Group Databasebeta

C2×C32×(C2×D3)⋊C8 #13162543

order1728
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C32×C8 · Schur multiplier (H2) = C24×C3

Aliases

direct productC2×C32×(C2×D3)⋊C8

Splittings

FittingC22×C33×C8 ⋊ C2
SylowC33 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC22×C32×C4C2×D3
commutatorC2×C3C22×C32×C8
FrattiniC2×C4C22×C32×D3
FittingC22×C33×C8C2
socleC23×C33C2×C4
prime radicalC23×C32×D3C4
cosocleC2×C3×C4C23×C32
hypercenterC22×C32×C8D3
hypocenterC3C2×C32×C22⋊C8
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C32×C4 ◁ C22×C32×C8

1516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 28606);